Question

Find the constants A and B that makes the given equation true. How do I solve for this?

Answer 1

\[\frac{3x+15}{x^2-4x-5}=\frac{a}{x-50}+\frac{b}{x+1}\]

Answer 2

@zepdrix @dan815

Answer 3

I don't know where to start with this equation..

Answer 4

@jim_thompson5910

Answer 5

Multiply to get the denominators equal first. You are on the right track.

2x-9/(x^2-x-6) = A/(x-3) + B/(x+2)

Multiply A by (x+2)/(x+2) and B by (x-3)/(x-3). Now all have the same denominator, so you can ignore the denominator when solving for A and B.

Now you have...

2x-9 = A(x+2) + B(x-3)

Distribute...

2x-9 = Ax + 2A + Bx - 3B

Separate into two equations, one for X and one for your constants.

2x = Ax + Bx
-9 = 2A - 3B

Solve this system of equations. You can drop the x's out of the first equation because there is one in every term.

2 = A + B
-9 = 2A - 3B

Multiply the first equation by 3 and add to the second to cancel out the B's.

6 = 3A + 3B Add
-9 = 2A - 3B +
___________

-3 = 5A

A = -3/5.

Plug this back into any of the two equations.

2 = A + B ===> 2 = -3/5 + B

13/5 = B

So, A = -3/5. and B = 13/5.

Answer 6

Is This Helpful??

Answer 7

wOw thank you so much! I was taking my time to process the stuff. U r a lifesaver :D

Answer 8

your welcome!!!

Answer 9

I really appreciate your time and effort to help me!

Answer 10

yo @jim_thompson5910 thanks for coming by

Answer 11

Also I mistyped the problem but I understand how to solve

Answer 12

it suppose to be (x-5) not (x-50)

Answer 13

Here is another route

2x-9 = A(x+2) + B(x-3)
2(-2)-9 = A(-2+2) + B(-2-3) .... plug in x = -2
-4-9 = A*0+B(-5)
-13 = -5B
-13/(-5) = B
B = 13/5

Now use this to find A.
You'll find that A = -3/5

Answer 14

Oh okey so just use x to get ride of one of the variables. Gotcha!

Answer 15

@Victoriasushchik has the more effective method though