Question

Simplify completely quantity 5 x squared plus 9 x minus 2 over quantity x squared plus 12 x plus 20 times quantity x squared plus 17 x plus 70 over quantity 15 x minus 3

Answer 1

\[\large \frac{5x^2 + 9x - 2}{x^2 + 12x + 20} \times \frac{x^2 + 17x + 70}{15x - 3}\]

Like that right?

Answer 2

yes that looks right

Answer 3

Well this can be simplified a lot through factorization ...as in

So using factorization...how can we simplify (lets do...)

x^2 + 17x + 70

?

Answer 4

(x+7)(x+10)?

Answer 5

Perfect...alright so we'll put that to the side for now...how about

x^2 + 12x + 20

?

Answer 6

(x+2)(x+10)

Answer 7

Good again...now

15x - 3

? what number can be factored out?

Answer 8

3(5x-1)

Answer 9

Doing awesome!

and finally

5x^2 + 9x - 2

?

Answer 10

gosh I hate these higher coefficients give me a min

Answer 11

Of course :)

Answer 12

(5x-1)(x+2) sorry finally haha

Answer 13

Perfect! and I was gonna say you do know the fast way to do those right? But alright good :)

Answer 14

So now...altogether we have

\[\large \frac{(5x - 1)(x + 2)}{(x + 10)(x + 2)} \times \frac{(x + 10)(x + 7)}{3(5x - 1)}\]

Answer 15

Since this is multiplication...we can just combine these over 1 fraction...

\[\large \frac{(5x - 1)(x + 2)(x + 10)(x + 7)}{(x + 10)(x + 2)3(5x - 1)}\]

Answer 16

Now we can begin to cancel...what is on the top as well as the bottom...I see a bunch

\[\large \frac{\cancel{(5x - 1)}(x + 2)(x + 10)(x + 7)}{(x + 10)(x + 2)3\cancel{(5x - 1)}}\]

Answer 17

\[\large \frac{\cancel{(5x - 1)}\cancel{(x + 2)}(x + 10)(x + 7)}{(x + 10)\cancel{(x + 2)}3\cancel{(5x - 1)}}\]

Answer 18

\[\large \frac{\cancel{(5x - 1)}\cancel{(x + 2)}\cancel{(x + 10)}(x + 7)}{\cancel{(x + 10)}\cancel{(x + 2)}3\cancel{(5x - 1)}}\]

Answer 19

So all that is left is

\[\large \frac{x + 7}{3}\]

Answer 20

Sweet! I actually understand that. The quiz I needed it for is long finished but I'm really glad I got to go back through it. Thank you so much! You've been a great help. :)

Answer 21

Anytime hun :)