Question

How do you divide and simplify `\frac { x + 1} { 4x + y } \div \frac { 3x ^ { 2} - x - 4} { 16x ^ { 2} - y ^ { 2} }`?

Answer 1

(4x+y)/(3x-4)

Explanation:

When dividing by a factor `a/b`, it is the same as multiplying by `b/a`. That in mind...

`(x+1)/(4x+y)div(3x^2-x-4)/(16x^2-y^2)= (x+1)/(4x+y)*(16x^2-y^2)/(3x^2-x-4)`.

Factoring the right hand term gives us:

`(x+1)/(4x+y)times(16x^2-y^2)/(3x^2-x-4)` `= (x+1)/(4x+y)times((4x+y)(4x-y))/((3x-4)(x+1)`.

The `x+1` and `4x+y` terms cancel out, leaving...

`(x+1)/(4x+y)times((4x+y)(4x-y))/((3x-4)(x+1)) = (4x-y)/(3x-4)`