Question

How do you multiply and simplify `\frac { 15x ^ { 2} - 960} { x ^ { 2} + 13x + 40} \cdot \frac { x ^ { 2} - 25} { x ^ { 5} - 13x ^ { 4} + 40x ^ { 3} }`?

Answer 1

`15/x^3`

Explanation:

Factorise:
`15x^2-960=15(x^2-64)=15(x-8)(x+8)`
`x^2-25=(x-5)(x+5)`
`x^2+13x+40=(x+8)(x+5)`
`x^5-13x^4+40x^3=x^3(x-5)(x-8)`
Our original expression becomes:
`(15(x-8)(x+8))/((x+8)(x+5))*((x-5)(x+5))/(x^3(x-5)(x-8))`

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