Question

what is the sum? (\frac{3x}{x - 4}+\frac{x - 3}{2x}) options: (\frac{6x^4 - 7x + 12}{2x(x - 4)}), (\frac{7x^2 - 7x + 12}{2x(x - 4)}), (\frac{7x^2 + 7x + 12}{2x(x - 4)}), (\frac{6x^4 + 7x + 12}{2x(x - 4)})

Explanation:

Step1: Find common denominator

The denominators are $x-4$ and $2x$, so the common denominator is $2x(x-4)$.

Step2: Rewrite each fraction

$\frac{3x}{x-4} = \frac{3x \cdot 2x}{2x(x-4)} = \frac{6x^2}{2x(x-4)}$
$\frac{x-3}{2x} = \frac{(x-3)(x-4)}{2x(x-4)} = \frac{x^2 -7x +12}{2x(x-4)}$

Step3: Add the numerators

$\frac{6x^2 + x^2 -7x +12}{2x(x-4)}$

Step4: Combine like terms

$\frac{7x^2 -7x +12}{2x(x-4)}$

Answer:

$\frac{7x^2 -7x +12}{2x(x-4)}$