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Revision:Algebraic Fractions

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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Algebraic Fractions

 
 
Algebraic Fractions

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When adding or subtracting algebraic fractions, the first thing to do is to put them onto a common denominator (by cross multiplying).

e.g. \displaystyle \frac{1}{x+1} + \frac{4}{x+6}

\displaystyle = \frac{1(x+6)}{(x+1)(x+6)} + \frac{4(x+1)}{(x+1)(x+6)} = \frac{(x+6) + (4x+4)}{(x+1)(x+6)}

\displaystyle = \frac{5x+10}{(x+1)(x+6)} = \frac{5(x+2)}{(x+1)(x+6)}

Solving equations

When solving equations containing algebraic fractions, first multiply both sides by an expression which removes the fractions.

Example:

Solve \displaystyle \frac{10}{x+3} - \frac{2}{x} = 1.

Multiply both sides by x(x + 3):

\displaystyle \frac{10x(x+3)}{x+3} - \frac{2x(x+3)}{x} = x(x+3)

\displaystyle 10x - 2(x+3) = x(x+3)

\displaystyle 8x - 6 = x^2 + 3x

\displaystyle x^2 - 5x + 6 = 0 \Rightarrow x=2,3


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