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a - 3b   +    a + 5b

a + b          a + b

 Jan 11, 2018

Best Answer 

 #1
avatar+8961 
+1

\(\frac{a-3b}{a+b}\,+\,\frac{a+5b}{a+b}\)

                             These fractions have a common denominator so we can combine them.

\(=\,\frac{(a-3b)+(a+5b)}{a+b} \\~\\ =\,\frac{a-3b+a+5b}{a+b} \\~\\ =\,\frac{a+a+5b-3b}{a+b} \\~\\ =\,\frac{2a+2b}{a+b}\)

                             Let's factor a  2  out of the numerator.

\(=\,\frac{2(a+b)}{a+b}\)

                             Now we can reduce the fraction by  (a+b) .

\(=\,2\)                     This is true for all values of  a  and  b  as long as  a + b ≠ 0 .

 Jan 11, 2018
 #1
avatar+8961 
+1
Best Answer

\(\frac{a-3b}{a+b}\,+\,\frac{a+5b}{a+b}\)

                             These fractions have a common denominator so we can combine them.

\(=\,\frac{(a-3b)+(a+5b)}{a+b} \\~\\ =\,\frac{a-3b+a+5b}{a+b} \\~\\ =\,\frac{a+a+5b-3b}{a+b} \\~\\ =\,\frac{2a+2b}{a+b}\)

                             Let's factor a  2  out of the numerator.

\(=\,\frac{2(a+b)}{a+b}\)

                             Now we can reduce the fraction by  (a+b) .

\(=\,2\)                     This is true for all values of  a  and  b  as long as  a + b ≠ 0 .

hectictar Jan 11, 2018
 #2
avatar
+1

Thank you!!! 

Guest Jan 11, 2018

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