# Algebra

x/(x-3)-4-(2x-5)/(x+2)

If the problem is this:

x/(x - 3) - 4 - (3x - 5)/(x + 2)

...find a common denominator to start.

The common denominator is (x - 3)(x + 2), then convert each term using the common denominator.

Here's a start:

[x(x + 2)/(x - 3)(x + 2)] - [4(x - 3)(x + 2)]/(x - 3)(x + 2) - [(2x - 5)(x - 3)]/(x - 3)(x + 2) =

I'll let you take it from here. Remember to use the distributive property to distribute the negative!

I hope this will help and is what you were asking.

One correction!

I meant to type this for the problem:

x/(x - 3) - 4 - (2x - 5)/(x + 2)

The rest is OK. Sorry for any confusion!

but when I do this I get

x^2+2x-4x^2+4x+24-2x^2+x+15

solving this I get

(-5x^2+7x+39)/(x-3)(x+2)

The answer in the book however says

-(5x^2-17x-9)/(x-3)(x+2)

so I don't know what I am doing wrong, can you take me step by step through the problem. I have a lot of problems, but I think once I understand what I am doing wrong with this one I can get the rest.

The top should be this:

x^2 + 2x - 4x^2 + 4x + 24 - 2x^2 + 11x - 15

Combining like terms:

-5x^2 + 17x + 9

Factoring out the negative gives this:

-(5x^2 - 17x - 9)

-(5x^2-17x-9)/(x-3)(x+2)

I hope this helps. Watch those negative signs because they can be tricky on these types of problems!

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