Question

Solve for $x$: $\frac{4}{x} - 3 = \frac{5}{2x + 3}, x 
eq 0, -\frac{3}{2}$.

Accepted Answer

$\frac{4 - 3x}{x} = \frac{5}{2x + 3} \implies (4 - 3x)(2x + 3) = 5x$ $8x + 12 - 6x^2 - 9x = 5x \implies 12 - x - 6x^2 = 5x$ $6x^2 + 6x - 12 = 0 \implies x^2 + x - 2 = 0$ $(x + 2)(x - 1) = 0 \implies x = 1 	ext{ or } x = -2$.

Solve rational equation

Explanation

Practise this under board exam conditions