Coaching Centre
Equations with fractions
Solving equations with algebraic fractions by multiplying both sides, including fractions on both sides and cross-multiplying.
Clearing fractions
Solve $\dfrac{x + 4}{3} = 5$.
$x + 4 = 15$
Multiply both sides by 3
$x = 11$
Solve $\dfrac{x}{3} + 2 = 6$.
$\dfrac{x}{3} = 4$
$x = 12$
A fraction on each side
Solve $\dfrac{x + 1}{2} = \dfrac{x + 5}{4}$.
$2(x + 1) = x + 5$
Multiply both sides by 4 (the LCD)
$2x + 2 = x + 5$, so $x = 3$
$dfrac{x}{5} = 3$
$x = 15$
Fraction on each side
Multiply both sides by the lowest common denominator.
$dfrac{x - 1}{2} = 4$
$x = 9$
Solve $\dfrac{x + 4}{3} = 5$.
$x + 4 = 15$.
Solve $\dfrac{x}{3} + 2 = 6$.
$\dfrac{x}{3} = 4$.
Solve $\dfrac{x + 1}{2} = \dfrac{x + 5}{4}$.
$2x + 2 = x + 5$.
Solve $\dfrac{x - 1}{2} = 4$.
$x - 1 = 8$.
Solve $\dfrac{3x}{5} = 6$.
$3x = 30$.
Solve $\dfrac{x}{2} - 1 = -4$.
$\dfrac{x}{2} = -3$.
Solve $\dfrac{2x + 1}{5} = 3$.
$2x + 1 = 15$.
Solve $\dfrac{x}{2} = \dfrac{x}{3} + 1$.
Multiply by $6$: $3x = 2x + 6$.
New numbers every time. Keep going until you get five in a row.