SOLUTION: Problem is solving for X. (rational equation) There should be a line under each one (between x+4 and x+5 and then another between x-2 and x+4) with ONE equal sign. x+4 = x-2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Problem is solving for X. (rational equation) There should be a line under each one (between x+4 and x+5 and then another between x-2 and x+4) with ONE equal sign. x+4 = x-2       Log On


   

Question 335132: Problem is solving for X. (rational equation)
There should be a line under each one (between x+4 and x+5 and then another between x-2 and x+4) with ONE equal sign.
x+4 = x-2
x+5 = x+4
Thanks in advance!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
I presume you mean the following:

%28x%2B4%29%2F%28x%2B5%29+=+%28x-2%29%2F%28x%2B4%29

If you cross multiply, you get:

%28x%2B4%29%5E2+=+%28x-2%29+%2A+%28x%2B5%29

If you multiply these out, you will get:

x%5E2+%2B+8x+%2B+16+=+x%5E2+%2B+3x+-+10

If you subtract the expression on the right side of the equation from both sides of the equation, then you will get:

x%5E2+%2B+8x+%2B+16+-+x%5E2+-+3x+%2B+10+=+x%5E2+%2B+3x+-+10+-+x%5E2+-+3x+%2B+10

When you combine like terms, you will get:

5x+%2B+26+=+0

If you subtract 26 from both sides of this equation, you will get:

5x+=+-26

If you divide both sides of this equation by 5, you will get:

x = -26/5

That should be your answer.

Substitute for x in your original equation to see if it comes out true.

You start with %28x%2B4%29%2F%28x%2B5%29+=+%28x-2%29%2F%28x%2B4%29.

Since -26/5 = -5.2, then you replace x with -5.2 to get:

%28-5.2%2B4%29%2F%28-5.2%2B5%29+=+%28-5.2-2%29%2F%28-5.2%2B4%29.

This becomes:

%28-1.2%29%2F%28-.2%29+=+%28-7.2%29%2F%28-1.2%29 which becomes:

6+=+6 which is true, confirming that your answer of x = -26/5 = -5.2 is correct.