SOLUTION: The denominator of a fraction is 2 more than the numerator. If 1 is added to both the fraction reduces to 4/5. Find the fraction.

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Question 1055439: The denominator of a fraction is 2 more than the numerator. If 1 is added to
both the fraction reduces to 4/5. Find the fraction.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the number in the numerator
The unknown fraction is:
+x+%2F+%28+x+%2B+2+%29+
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Add +1+ to both numerator and denominator
+%28+x+%2B+1+%29+%2F+%28+x+%2B+2+%2B+1+%29+=+4%2F5+
+%28+x+%2B+1+%29+%2F+%28+x+%2B+3+%29+=+4%2F5+
Multiply both sides by +5%2A%28+x+%2B+3+%29+
+5%2A%28+x+%2B+1+%29+=+4%2A%28+x+%2B+3+%29+
+5x+%2B+5+=+4x+%2B+12+
+x+=+7+
-----------------
+x+%2F+%28+x+%2B+2+%29+=+7+%2F+%28+7+%2B+2+%29+
+x+%2F+%28+x+%2B+2+%29+=+7+%2F+9+
The fraction is 7/9
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check:
+%28+x+%2B+1+%29+%2F+%28+x+%2B+3+%29+=+4%2F5+
+%28+7+%2B+1+%29+%2F+%28+7+%2B+3+%29+=+4%2F5+
+8%2F10+=+4%2F5+
+4%2F5+=+4%2F5+
OK