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