Question

How do you multiply and simplify `\frac { 5x ^ { 2} - 8x - 4} { 5x ^ { 2} - 7x - 6} \cdot \frac { x ^ { 2} - 16} { 5x ^ { 2} + 22x + 8}`?

Answer 1

`(x-4)/(5x+3)`

Explanation:

`"factorise numerators/denominators and cancel any"`
`"common factors"`

`rArr(cancel((5x+2))cancel((x-2)))/((5x+3)cancel((x-2)))xx((x-4)cancel((x+4)))/(cancel((5x+2))cancel((x+4)))`

`=(x-4)/(5x+3)to(x!=-3/5)`

Answer 2

See below.

Explanation:

`(5x^2-8x-4)/(5x^2-7x-5)*(x^2-16)/(5x^2+33+8)`

Factor numerators and denominators:

`x^2-16=(x+4)(x-4)` ( difference of two squares )

`((5x+2)(x-2))/((5x+3)(x-2))*((x+4)(x-4))/((5x+2)(x+4))`

Cancelling like factors:

`(cancel((5x+2))cancel((x-2)))/((5x+3)cancel((x-2)))*(cancel((x+4))(x-4))/(cancel((5x+2))cancel((x+4)))=(x-4)/(5x+3)`