Question

Find and simplify the quotient (image provided)

Answer 1

Explanation:

The difference quotient is defined as

`(f(x + h) - f(x))/(h)`

The term

`f(x + h)`

means everywhere we see a (x), replace it with (x+h)

So

we get

`\frac{9 + 5(x + h) - 6(x + h) {}^(2) - (9 + 5x - 6 {x}^(2)) }{h}`

`\frac{9 + 5x + 5h - 6 {x}^(2) - 12hx - 6 {h}^(2) - (9 + 5x - 6 {x}^(2) ) }{h}`

`\frac{5h - 12hx - 6 {h}^(2) }{h}`

`5 - 12x - 6h`