Express $\displaystyle ax+b+  \frac{dx+p}{x + q}$ as an algebraic single fraction. 

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

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Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

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The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

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

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.

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

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$. Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$.

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Contains a video solving a similar quotient rule example. Although does not explicitly find $g(x)$ as asked in the question, but this is obvious.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

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

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.

Algebraic manipulation/simplification.

Simplify $\displaystyle \frac{ax^4+bx^2+c}{a_1x^4+b_1x^2+c_1}$ by cancelling a a common degree 2 factor.

Express a sum of linear terms in $x$ and $y$ as a single linear term in $x$ and $y$.

Expand $(ay+b)(cy+d)(py+q)$.

Includes a video expanding three brackets, however uses the variable $x$ rather than $y$.

Expand $ax(cx+d)$ and expand $(rx+s)(px)$

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

Expand $(pw+q)(aw^2+bw+c)$.

Expand $(az^2+bz+c)(pz+q)$.

Expand $(az^2+bz+c)(dz^2+pz+q)$.

Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$. Answer is a multiple of $x$.