Question

Simplify completely quantity 2 x squared plus 16 x plus 30 all over quantity 5 x squared plus 13 x minus 6.

2 open parentheses x plus 3 close parentheses over quantity 5 x minus 1
2 open parentheses x plus 3 close parentheses over quantity 5 x minus 6
2 open parentheses x plus 5 close parentheses over quantity 5 x minus 2
2 open parentheses x plus 5 close parentheses over quantity 5 x minus 3

Answer 1

(2x^2 + 16x + 30) / (5x^2 + 13x -6)
Start by factoring the numerator and denominator.
Cancel any like factors.

2(x^2 + 8x + 15)
2(x + 5)(x + 3) / (5x -2)(x + 3
2(x + 5) / (5x - 2)
The third choice

Answer 2

Answer: Third option is correct.

Explanation:

Since we have given that

Quantity 2 x squared plus 16 x plus 30 all over quantity 5 x squared plus 13 x minus 6 i.e.

`(2x^2+16x+30)/(5x^2+13x-6)`

We just need to simplify the numerator and denominator :

1) Simplify the numerator by using the Splitting the middle terms:

`2x^2+16x+30\\\\=2x^2+10x+6x+30\\\\=2x(x+5)+6(x+5)\\\\=(2x+6)(x+5)\\\\=2(x+3)(x+5)`

2) Simplify the denominator by using the Splitting the middle terms:

`5x^2+13x-6\\\\=5x^2+15x-2x-6\\\\=5x(x+3)-2(x+3)\\\\=(5x-2)(x+3)`

Now, we use the both results in the expression:

`(2(x+3)(x+5))/((5x-2)(x+3))\\\\=(2(x+5))/(5x-2)`

So, 2 open parentheses x plus 5 close parentheses over quantity 5 x minus 2.

Hence, Third option is correct.