Question

What is the simplified form of the quantity of x plus 5, all over the quantity of 3x plus 4 + the quantity of x plus 4, all over the quantity of x plus 3?

the quantity of 2x plus 9, all over the quantity of 4x plus 7
the quantity of 4x squared plus 24x plus 31, all over the quantity of 3x squared plus 13x plus 12
the quantity of 4x squared plus 24x plus 31, all over the quantity of 4x plus 7
the quantity of 2x plus 9, all over the quantity of 3x squared plus 13x plus 12

Answer 1

I know it is either b or c, i just cannot conclude the denominator.

Answer 2

how do you know it's b or c ?

Answer 3

i used a calculator and the numerator came up accordingly in relation to the answers, however the denominator did not.

Answer 4

I would (did) multiply the two bottom denominators to get a "common denominator"

To add fractions, you want both to have the same denominator.

I would multiply the first fraction by (x+3)/(x+3)
and the 2nd by (3x+4)/(3x+4)

Answer 5

the bottom will be (x+3)(3x+4) = 3x^2 +9x+4x+12 = 3x^2+13x+12

Answer 6

i got that.

Answer 7

Im thinking its letter choice B.

Answer 8

For the top, we do the first fraction
(x+5)(x+3) = x^2 + 8x +15

and the 2nd fraction
(x+4)(3x+4)= 3x^2 + 16x+16
and added together the top is
4x^2 +24x+31

Answer 9

Concluding to answer choice "B", correct?

Answer 10

yes, we get
\[ \frac{4x^2 +24x+31}{3x^2+13x+12}\]