+0

# Adding and subtracting rational expressions

0
371
3

a - 3b   +    a + 5b

a + b          a + b

Jan 11, 2018

#1
+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
+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 .

hectictar Jan 11, 2018