## 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, if then we can multiply both sides by to clear the fraction, obtaining Expanding the right hand side gives and 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, if then 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 by to clear the fractions, obtaining and expand the right hand side to give Move all the terms to the right hand side to give This expression does not factorise, so use the quadratic formula, In this case, and   