+0

# Adding and subtracting rational expressions

0
27
3

a - 3b   +    a + 5b

a + b          a + b

Guest Jan 11, 2018

#1
+5888
+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
Sort:

#1
+5888
+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
#2
+1

Thank you!!!

Guest Jan 11, 2018

### 18 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details