Question

Let f(x)=4x^2+3x−1/4x^2+9x+5 and g(x)=4x^2+7x−2/x^2−4. Simplify: f(x)÷g(x) f(x)÷g(x)=______

Answer 1

Answer:

$\frac{x-2}{4x+5}$

Step-by-step explanation:

Given

$\frac{4x^2+3x-1}{4x^2+9x+5}$ ÷ $\frac{4x^2+7x-2}{x^2-4}$

Factorise numerator / denominator of both fractions

= $\frac{(4x-1)(x+1)}{(4x+5)(x+1)}$ ÷ $\frac{(4x-1)(x+2)}{(x-2)(x+2)}$

Cancel common factors on numerator/ denominator of both fractions

= $\frac{4x-1}{4x+5}$ ÷ $\frac{4x-1}{x-2}$

Change ÷ to × and turn second fraction upside down

= $\frac{4x-1}{4x+5}$ × $\frac{x-2}{4x-1}$

Cancel the common factor 4x - 1 on numerator/ denominator, leaving

$\frac{x-2}{4x+5}$