Question

Express {x}{x+2} +\frac{2x}{x-4}" alt="\frac{x}{x+2} +\frac{2x}{x-4}" align="absmiddle" class="latex-formula">as a single fraction in its simplest form.

Answer 1

Answer:

$\frac{3x^2}{(x+2)(x-4)}$

Step-by-step explanation:

Before adding the fractions we require them to have a common denominator.

Multiply numerator/ denominator of first fraction by x - 4

Multiply numerator/ denominator of second fraction by x + 2

= $\frac{x(x-4)}{(x+2)(x-4)}$ + $\frac{2x(x+2)}{(x+2)(x-4)}$ ← expand and simplify numerators, leaving common denominator

= $\frac{x^2-4x+2x^2+4x}{(x+2)(x-4)}$

= $\frac{3x^2}{(x+2)(x-4)}$