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
