SOLUTION: Solve fractional equation: 6/ x-3 - 5/x+1 = 7/x^2-2x-3

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Solve fractional equation: 6/ x-3 - 5/x+1 = 7/x^2-2x-3       Log On


   

Question 1105252: Solve fractional equation: 6/ x-3 - 5/x+1 = 7/x^2-2x-3
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


We know what the equation is supposed to be; it would be nice if you showed it to us correctly. As another tutor here likes to say, "Parentheses are free. Use them."

Here is the equation you show:
6%2F+x-3+-+5%2Fx%2B1+=+7%2Fx%5E2-2x-3

Obviously the equation is supposed to be
6%2F%28x-3%29+-+5%2F%28x%2B1%29+=+7%2F%28x%5E2-2x-3%29

The denominator of the fraction on the right is the least common denominator for all three fractions. So multiply both sides of the equation by that least common denominator to clear the fractions.


6%28x%2B1%29+-+5%28x-3%29+=+7
6x%2B6-5x%2B15+=+7
x%2B21+=+7
x+=+-14

CHECK:

6%2F%28-14-3%29+-+5%2F%28-14%2B1%29+=+7%2F%28%28-14%29%5E2-2%28-14%29-3%29
-6%2F17+%2B+5%2F13+=+7%2F221
-6%2813%29+%2B+5%2817%29+=+7
-78+%2B+85+=+7
7+=+7