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Practice with adding, subtracting and dividing basic algebraic fractions

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Express the following as a single fraction and simplify where possible.

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Remember to use brackets appropriately and to use a * for multiplication for letters.

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See Lecture 4.1 and Workshop 4.2 for background and examples.

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For background on fractions see 2.3.  For background on algebraic manipulations see 2.6 and 3.3.

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a/x  + 1/bx

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c/x - a/d

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a/x * d/by

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d/x  /   c/ay

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a/x -  1 / (c-fx)

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c/(d + y) - (b)/(a+ x)

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\\[ \\frac{\\var{a}}{x} + \\frac{1}{\\var{b}x} \\]

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\\[ \\frac{\\var{c}}{x} - \\frac{\\var{a}}{\\var{d}} \\]

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\\[ \\frac{\\var{a}}{x} \\times \\frac{\\var{d}}{\\var{b}y} \\]

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\\[ \\frac{\\var{d}}{x} \\div \\frac{\\var{c}}{\\var{a}y} \\]

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\\[ \\dfrac{\\var{a}}{x} + \\dfrac{1}{(\\var{c} -\\var{f}x)} \\]

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\\[ \\frac{\\var{c}}{(\\var{d} + y)} - \\frac{\\var{b}}{(\\var{a} + x)}\\]

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Have you checked that you have entered answers appropriately: used brackets and * where necessary.

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