Want to double check if I solved this correctly?

Question

3 over x+7 minus -1 over x+2 equals 5 over x^2+9x+14

I factored x^2+9x+14 into (x+7)(x+2) and multiplied both sides with it, leaving me with:

3x+6+x+7=5

3x+13=5

4x=18

x=18 over 4?

Answer 1

Favorite Answer

I am affraid thats wrong..

you did a common mistake and you should not feel bad about it.

the R.H.S is ok

lets work with the L.H.S

3x+6+x+7=5 this is where you got wrong

in fact you got this from

3 * ( x + 2 ) - ( x + 7)

it should be

3x + 6 - x - 7

so

3x + 6 - x - 7 = 5

and the answer is x = 3

note that -a * ( b + c) = -ab - c

and -a * ( b - c ) = -ab + ac

L.H.S = lift hand side

R.H.S = right """"""

* means multiplication

forgive me my english is week

Answer 2

Jerome: 18/4 is not the same as 3 (maybe you saw 18 over 6?)

there is something not clear with your question, you say "minus -1"

written that means -(-1), but did you mean simply -1 ?

1. if you meant simply -1 then Jerome is right, the answer is 3

2. if the problem is -(-1), in other words

3/(x + 7) - [-1/(x + 2)] = 5/(x^2 + 9x + 14)

then you were on the right track but made a small mistake, 13 is supposed to be subtracting on the other side, thus

4x = 5-13

4x = -8

x = -2

but that is impossible since you have a x+2 as denominator which would mean that there is no solution to the equation

(the same way there is no solution for 1/x=0)

this makes me think that you meant simply -1 from the beginning, but i'm covering all possibilities

Source(s): myself

Answer 3

3/(x + 7) - 1/(x + 2) = 5/(x² + 9x + 14)

3/(x + 7) - 1/(x + 2) = 5/[(x + 7)(x + 2)]

3(x + 2) - (x + 7) = 5

3x + 6 - x - 7 = 5

2x - 1 = 5

2x = 6

x = 6/2

x = 3

Verify the answer:

3/(x + 7) - 1/(x + 2) = 5/(x² + 9x + 14)

3/(3 + 7) - 1/(3 + 2) = 5/(3² + 9(3) + 14)

(3/10) - (1/5) = 5/(9 + 27 + 14)

(3/10) - (1/5) = 5/50

(3/10) - (2/10) = 1/10

1/10 = 1/10

Answer 4

{3 / (x + 7) } - { 1 / (x + 2) } = { 3 (x + 2) - 1 (x + 7) } / (x + 7) (x + 2)

The denominators are the same on both sides of the equation, so the numerators must also be equal.

So { 3 (x + 2) - 1 (x + 7) } = 5

3x + 6 - x - 7 = 5

2x - 1 = 5

x = 3

When you multiplied the left-hand side by (x + 7) (x + 2), you overlooked the minus sign of the second term, so your second line should be 3x + 6 - x - 7. There is nothing wrong with your method, I just preferred the approach I showed above.

Answer 5

I'll solve so you could compare

3/(x + 7) - 1/(x + 2) = 5/(x^2 + 9x + 14)

3(x + 2) - 1(x + 7) = 5

3x + 6 - x - 7 = 5

3x - x = 5 - 6 + 7

2x = 6

x = 6/2

x = 3

I got the same answer.