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

`(x-2)/(4x+5)`

Explanation:

Given

`(4x^2+3x-1)/(4x^2+9x+5)` ÷
`(4x^2+7x-2)/(x^2-4)`

Factorise numerator / denominator of both fractions

=
`((4x-1)(x+1))/((4x+5)(x+1))` ÷
`((4x-1)(x+2))/((x-2)(x+2))`

Cancel common factors on numerator/ denominator of both fractions

=
`(4x-1)/(4x+5)` ÷
`(4x-1)/(x-2)`

Change ÷ to × and turn second fraction upside down

=
`(4x-1)/(4x+5)` ×
`(x-2)/(4x-1)`

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

`(x-2)/(4x+5)`