Simplify quantity 4 x squared plus 12 x minus 16 all over quantity 2x plus 10 over quantity 6 x plus 24 over quantity x squared

Question

4 years ago

9

plus 9x plus 20

2 answers:

Softa [21] · Answer 1 · 2021-11-16T01:10:03+03:00

Softa [21]4 years ago

6 0

The answer is: (x-1)(x+4)/3
hope this helped! (:

ladessa [460] · Answer 2 · 2021-11-16T03:29:37+03:00

$\frac{4x^2+12x-16}{\frac{2x+10}{\frac{6x+24}{x^2+9x+20}}}$

Here we have two fractions top and bottom

$\frac{4x^2+12x-16}{2x+10}$ divide by $\frac{6x+24}{x^2+9x+20}$

We have division in between . we reverse the second fraction and multiply it with first fraction.

$\frac{4x^2+12x-16}{2x+10}$ * $\frac{x^2+9x+20}{6x+24}$

Now we factor both numerator and denominator

4x^2+12x-16 = 4 (x+4)(x-1)

2x+10 = 2(x+5)

x^2+9x+20 = (x+5)(x+4)

6x+24 = 6(x+4)

Replace the factors,

$\frac{4 (x+4)(x-1)}{2(x+5)}$ * $\frac{(x+5)(x+4)}{6(x+4)}$

We cancel out same factors at the top and bottom

So it becomes , $\frac{(x-1)(x+4)}{3}$