Question

How do you multiply and divide `\frac { 7x } { x ^ { 2} + 5x + 4} \cdot \frac { x ^ { 2} - 16} { x ^ { 2} + 2x } \div \frac { x - 4} { x + 1}`?

Answer 1

`7/(x+2)`

Explanation:

`(7x)/(x^2+5x+4) . (x^2-16)/(x^2+2x) . (x+1)/(x-4)`

`(7x)/((x+1)(x+4)).(x^2-16)/(x^2+2x) . (x+1)/(x-4)`

`(7x)/((x+1)(x+4)).((x+4)(x-4))/(x(x+2) ). (x+1)/(x-4)`

`(7cancelxcancel((x+4))cancel((x+4))cancel((x-4))cancel((x+1)))/(cancel((x+1))cancel((x+4))cancel((x+4))cancelx(x+2)cancel((x-4)))`

`7/(x+2)`