SOLUTION: 3/(x+1) +4/(x-2)=(px+q)/(x+1)(x-2) What is the value of p and q?

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Question 287802: 3/(x+1) +4/(x-2)=(px+q)/(x+1)(x-2)
What is the value of p and q?

Found 4 solutions by mananth, ikleyn, MathTherapy, KMST:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
3/(x+1) +4/(x-2)=(px+q)/(x+1)(x-2)
3(x-2)+4(x+1)= (px+q)(x+1)(x-2)/(x+1)(x-2)
3x-6+4x+4 = (px+q)
7x-2 = px+q
q=(7x-2)-px
p=(7x-2)-q /x

Answer by ikleyn(53875)   (Show Source):
You can put this solution on YOUR website!
.
3/(x+1) +4/(x-2)=(px+q)/(x+1)(x-2)
What is the value of p and q?
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        The answer in the post by @mananth is incorrect.
        I came to bring a correct solution.

3/(x+1) +4/(x-2)=(px+q)/(x+1)(x-2)

Multiply both sides by (x+1)*(x-2).
You will get an equivalent equality

3(x-2)+4(x+1)= (px+q)(x+1)(x-2)/(x+1)(x-2)
3x-6+4x+4 = (px+q)
7x-2 = px+q

Hence, p = 7, q = -2.

ANSWER.   p = 7,   q = -2.

At this point, the solution is complete.

Answer by MathTherapy(10839)   (Show Source):
You can put this solution on YOUR website!

3/(x+1) +4/(x-2)=(px+q)/(x+1)(x-2) What is the value of p and q? ***************************** Let's focus on the LEFT-SIDE of the equation ---- Multiplying left-side by GCF (x + 1)(x - 2) 7x - 2 = px + q --- Equating NUMERATORS, since DENOMINATORS are equivalent 7x = px - 2 = q ____7 = p

Answer by KMST(5377)   (Show Source):
You can put this solution on YOUR website!
If must be true for every value of ,
it will be true for and for .

For :

Multiplying times we get
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For :

Multiplying times we get

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