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Combining algebraic fractions 3.0
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Express $\displaystyle b+ \frac{dx+p}{x + q}$ as an algebraic single fraction.
Combining algebraic fractions 3.1
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Express $\displaystyle ax+b+ \frac{dx+p}{x + q}$ as an algebraic single fraction.
Combining algebraic fractions 3.2
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Express $\displaystyle \frac{ax+b}{x + c} \pm \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator.
Combining algebraic fractions 4
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Express $\displaystyle \frac{ax+b}{cx + d} \pm \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator.
Complete the square
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $B$ and $C$ such that $x^2+bx+c = (x+B)^2+C$ .
Complete the square
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $a$ , $B$ and $C$ such that $ax^2+bx+c = a(x+B)^2+C$ .
Differentation: Product Rule
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1} e ^ {n x}g(x)$ .
Differentiate product of binomial and exponential
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the function $(a + b x)^m e ^ {n x}$ using the product rule.
Differentiation: Product rule
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $f(x) = x^m(a x+b)^n$ .
Differentiation: Quotient rule
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$ . Find $g(x)$ .
Quotient rule - differentiate exponential over exponential
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$ . Find $p$ .
Quotient rule - differentiate linear over quadratic
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

The derivative of $\displaystyle \frac{ax+b}{cx^2+dx+f}$ is $\displaystyle \frac{g(x)}{(cx^2+dx+f)^2}$ . Find $g(x)$ .
Quotient rule - differentiate linear over square root
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$ . Find $g(x)$ .
Quotient rule - differentiate quadratic over quadratic
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$ . Find $g(x)$ .
Quotient rule - differentiate quotient of linear terms
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$ . Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$ .
Combining algebraic fractions
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$ .
Complete the square
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$ . Find both roots of the equation $q(x)=0$ .
Completing the square
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$ .
Divide Polynomials
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.
Solve an equation in logarithms
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$ .

Make sure that your choice is a solution by substituting back into the equation.
Solving equations
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Solve an equation with a reciprocal
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Expand product of brackets
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Expand $(ax+b)(cx+d)$ .
Lois's copy of Complete the square
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Question in Algebra by Lois Rollings

Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$ .
Divide Polynomials: Cubic by linear
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Question in Graphing and Polynomials by Ben Brawn

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.
Julie's copy of Algebra: Expansion of two brackets (one linear)
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Question in Julie's workspace by Julie Crowley

Expansion of two brackets

rebelmaths
Expansion of two brackets: Linear 2 positive coefficients
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Question in Julie's workspace by Julie Crowley

Expand $(ax+b)(cx+d)$ .

rebelmaths
Lois's copy of Combining algebraic fractions 3.1
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Question in Algebra by Lois Rollings

Express $\displaystyle ax+b+ \frac{dx+p}{x + q}$ as an algebraic single fraction.
Lois's copy of Test1: Combining algebraic fractions
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Question in Algebra by Lois Rollings

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$ .
Solving equations 2
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Question in Algebra by Lois Rollings

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$

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