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

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

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

You are given:

Notice that 5x + 10 can be factored by removing a 5 to make it 5(x+2). If you do this the equation becomes:

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 lacks a 5 in the denominator. Therefore, multiply this term by . This is equivalent to multiplying the second term by 1 because is 1. When you do this the equation becomes:

Finally, on the right side of the equation the denominator lacks the . Therefore, multiply the right side by [effectively multiplying it by 1. When you do that the equation becomes:

Now you can get rid of the common denominator entirely by multiplying all the terms in the equation by . This cancels out the denominator and leaves you with the equation:

Its all downhill from here. Just do the distributive multiplication on both sides to get:

Add the two terms containing x on the left side to get:

Add 15 to both sides:

Subtract 7x from both sides:

Multiply both sides by -1:

If you substitute this value for x in the original equation, you should find that it makes the left side of the equation equal to
Hope this helps.
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