Question

find the sum or difference

1. \\(\frac{2x}{x + 4} - \frac{3x + 4}{4x + 16}\\)

Explanation:

Step1: Simplify the second denominator

Factor out 4 from \(4x + 16\), we get \(4(x + 4)\). So the expression becomes \(\frac{2x}{x + 4}-\frac{3x + 4}{4(x + 4)}\).

Step2: Find a common denominator

The common denominator of \(x + 4\) and \(4(x + 4)\) is \(4(x + 4)\). Rewrite the first fraction: \(\frac{2x\times4}{4(x + 4)}-\frac{3x + 4}{4(x + 4)}=\frac{8x}{4(x + 4)}-\frac{3x + 4}{4(x + 4)}\).

Step3: Subtract the numerators

Subtract the numerators over the common denominator: \(\frac{8x-(3x + 4)}{4(x + 4)}\).

Step4: Simplify the numerator

Simplify the numerator: \(8x-3x - 4 = 5x - 4\). So the result is \(\frac{5x - 4}{4(x + 4)}\).

Answer:

\(\frac{5x - 4}{4(x + 4)}\)