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## Solving Equations Involving Algebraic Fractions

An algebraic fraction is any expression with fraction which include x terms in numerator and/or denominator. If this expression is equal to something then typically we can solve it by reararranging the fraction into a linear or quadratic equation and solving.

For example, ifthen we can multiply both sides byto clear the fraction, obtaining

Expanding the right hand side givesand collecting like terms gives

More complicated problems involve two fractions, which must be added first. Often a quadratic is obtained, which may solved by factorisation or use of the quadratic formula.

For example, ifthen we start by making a common denominator for the terms on the left hand side.

Now add the numerators to give

This is equal to the right hand side, so we can write

Multiply both sides byto clear the fractions, obtainingand expand the right hand side to give

Move all the terms to the right hand side to giveThis expression does not factorise, so use the quadratic formula,

In this case,and