SOLUTION: solve for the variable, first stating any restrictions. if there are no restrictions, state that 7/x+4 + 2/x-3 = 7x-21/x^2+x-12

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Question 232481: solve for the variable, first stating any restrictions. if there are no restrictions, state that
7/x+4 + 2/x-3 = 7x-21/x^2+x-12
Answer by eggsarecool(46) About Me  (Show Source):
You can put this solution on YOUR website!
I am assuming this is the original problem, it wasn't completely clear.
7%2F%28x%2B4%29+%2B+2%2F%28x-3%29+=+%287x-21%29%2F%28x%5E2%2Bx-12%29 the next step is to rewrite the right hand side.
7%2F%28x%2B4%29+%2B+2%2F%28x-3%29+=+%287x-21%29%2F%28x%2B4%29%28x-3%29 Now we state the restrictions, these happen when you divide by 0. So x cannot equal to 3 or -4
Your next step is to create a common denominator on the left side.

Now we will only pay attention to the numerators since the denominators match.
This gives us.
7x-21%2B2x%2B8=7x-21
Now combine like terms.
9x-13=7x-21
subtract 9x from both sides.
2x-13=-21
add 13 to both sides
2x=-8
Divide both sides by 2.
x=-4
This gives you the solution x=-4 but since this is among the values that are not allowed your equation has no solution.