SOLUTION: (x/5x+10)+((x-3)/(x+2))=7/5 Solve for x

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Question 69677: (x/5x+10)+((x-3)/(x+2))=7/5
Solve for x

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!

You are given:
x%2F%285x%2B10%29+%2B+%28x-3%29%2F%28x%2B2%29+=+7%2F5
Notice that 5x + 10 can be factored by removing a 5 to make it 5(x+2). If you do this the equation becomes:
x%2F5%28x%2B2%29+%2B+%28x-3%29%2F%28x%2B2%29+=+7%2F5
Next you need to make all the denominators the same. The common denominator is 5(x+2) so you don't need to do anything to the first term. It already has the common denominator. The second term %28x-3%29%2F%28x%2B2%29 lacks a 5 in the denominator. Therefore, multiply this term by 5%2F5. This is equivalent to multiplying the second term by 1 because 5%2F5 is 1. When you do this the equation becomes:
x%2F5%28x%2B2%29+%2B+5%28x-3%29%2F5%28x%2B2%29+=+7%2F5
Finally, on the right side of the equation the denominator lacks the x%2B2. Therefore, multiply the right side by %28x%2B2%29%2F%28x%2B2%29 [effectively multiplying it by 1. When you do that the equation becomes:
x%2F5%28x%2B2%29+%2B+5%28x-3%29%2F5%28x%2B2%29+=+7%28x%2B2%29%2F5%28x%2B2%29
Now you can get rid of the common denominator entirely by multiplying all the terms in the equation by 5%28x%2B2%29. This cancels out the denominator and leaves you with the equation:
+x+%2B+5%28x-3%29+=+7%28x%2B2%29
Its all downhill from here. Just do the distributive multiplication on both sides to get:
x+%2B+5x+-+15+=+7x%2B14
Add the two terms containing x on the left side to get:
6x+-+15+=+7x+%2B+14
Add 15 to both sides:
6x+=+7x+%2B+29
Subtract 7x from both sides:
-x+=+29
Multiply both sides by -1:
x+=+-29
If you substitute this value for x in the original equation, you should find that it makes the left side of the equation equal to7%2F5
Hope this helps.