Question

Simplify 2 over quantity x squared plus 8 x plus 15 end quantity plus 1 over quantity x squared plus 11 x plus 30 (1 point)

Answer 1

I would try to factor each of the quadratics as a first step to finding a common denominator

Answer 2

will you try it and tell me what to get because i can't seem to figure out anything

Answer 3

2 1
------------- = ---------------
x^2 +8x +15 x^2 +11x +30

so you know that

8= 5+3
15 = 5*3

and

11 = 6+5
30 = 6*5

can you make it now ?

Answer 4

so after i factor it what do you do

Answer 5

read what have wrote in the first line above @phi

ok ?

Answer 6

ok

Answer 7

actually not really. i really hate math and have no idea what to do. i factored it thats it

Answer 8

what do you have so far ?

Answer 9

((2)/(x+5)(x+3))+((1)/(x+6)(x+5))

Answer 10

next you need a common denominator. both have (x+5)
I would use
(x+5)(x+3)(x+6)

to get that denominator for the first fraction, multiply top and bottom by (x+6)
(but don't multiply it out, just write it down)

Answer 11

for the second fraction, multiply top and bottom by (x+3)

Answer 12

ok now what

Answer 13

what do you have so far ?

Answer 14

((2)(x+6)/(x+5)(x+3)(x+6))+((1)(x+3)/(x+6)(x+5)(x+3))

Answer 15

now both fractions have the same denominator, so that will be the denominator of the answer.

concentrate on just the tops:

2(x+6) + 1(x+3)

I would distribute the 2 in the first part, and simplify. can you do that ?

Answer 16

2x+12+x+3=2x^2+15

Answer 17

when you add, you can't get x^2

12+3 is 15 so that is ok

2x + x or (2x + 1x) means : you have 2 x's and add 1 more x. how many x's do you have?

Answer 18

3x

Answer 19

3x+15

Answer 20

so the top
2(x+6) + 1(x+3)

becomes
3x+15

can you factor 3 out of this ?

Answer 21

x+5

Answer 22

you write 3x+15 as 3(x+5)

so now you have the top as 3(x+5)

if we put that over the bottom, what do we get ?

Answer 23

3(x+5)/((x+6)(x+5)(x+3))

Answer 24

notice you have (x+5) in the top and bottom. anything divided by itself is 1, so you can simplify your answer.

Answer 25

3/(x+6)(x+3))

Answer 26

Finally, because anything divided by itself is 1 *except 0*, we do should make a note that x ≠ -5 because in the original, that would give us 0/0 which is undefined.

the final answer is
\[ \frac{3}{(x+6)(x+3)} \text{ , x≠ -5 } \]

x cannot be -6 or -3 either (no divide by 0), but we can see that just looking at the fraction

Answer 27

ok thanks so much for your help