SOLUTION: Solve: X x-3 7 ------ + ------ = --- 5x+10 x+2 5 DO I need to just figure out what x equals to figure get the 7/5? If so how do I go about

Algebra ->  Algebra  -> Equations -> SOLUTION: Solve: X x-3 7 ------ + ------ = --- 5x+10 x+2 5 DO I need to just figure out what x equals to figure get the 7/5? If so how do I go about      Log On

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Question 66393: Solve:
X x-3 7
------ + ------ = ---
5x+10 x+2 5
DO I need to just figure out what x equals to figure get the 7/5? If so how do I go about this because it could be many different solutions. Thank you
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
%28x%2F%285x%2B10%29%29+%2B+%28x-3%29%2F%28x%2B2%29+=+7%2F5 Multiply the second fraction by 5%2F5 to get the fractions over a common denominator.
x%2F%285x%2B10%29+%2B+5%28x-3%29%2F5%28x%2B2%29+=+7%2F5 Simplify.
x%2F%285x%2B10%29+%2B+%285x-15%29%2F%285x%2B10%29+=+7%2F5 Simplify.
%286x-15%29%2F%285x%2B10%29+=+7%2F5 Factor 5 in the denominator.
%286x-15%29%2F5%28x%2B2%29+=+7%2F5 Multiply both sides by 5.
%286x-15%29%2F%28x%2B2%29+=+7 Multiply both sides by (x+2)
6x-15+=+7%28x%2B2%29 Simplify.
6x-15+=+7x%2B14 Subtract 6x from both sides.
-15+=+x%2B14 Subtract 14 from both sides.
-29+=+x or x+=+-29
Check: Substitute x = -29.
%28x%2F%285x%2B10%29%29+%2B+%28x-3%29%2F%28x%2B2%29+=+%28-29%2F%285%28-29%29%2B10%29%29%2B%28-29-3%29%2F%28-29%2B2%29 Simplify.
%28-29%2F%28-145%2B10%29%29+%2B+%28-32%29%2F%28-27%29
%28%28-29%29%2F%28-135%29%29+%2B+%28-32%29%2F%28-27%29 Multiply the second fraction by 5%2F5 and drop the negative signs.
%2829%29%2F%28135%29+%2B+%28160%29%2F%28135%29 Add the fractions.
189%2F135 Reduce to simplest form.
189%2F135+=+7%2827%29%2F5%2827%29 = 7%2F5