How Do You Subtract Two Rational Expressions with the Same Denominator?

We're subtracting two rational expressions
The two rational expressions have common denominators of x-7, so we can just subtract the numerators
(2x+5) has a positive sign out front so we can just remove its parentheses
Now we just simplify the numerator

1. We're subtracting two rational expressions
1. Our rational expressions are 2x+4 over x-7 and 8x-10 over x-7
1. Our rational expressions are 2x+4 over x-7 and 8x-10 over x-7
2. x-7 is the common denominator
1. x-7 is the common denominator
2. The numerators are 2x+5 and 8x-10
1. To remove the parentheses we must distribute the signs in front of each one
1. To remove the parentheses we must distribute the signs in front of each one
1. Having a positive sign in front of the parentheses is just like multiplying by 1 so nothing on the inside changes
1. To remove the parentheses we must distribute the signs in front of each one
1. Having a negative sign in front of the parentheses is just like multiplying by -1 so the signs inside the parentheses are flipped
2. -1 • 8x = -8x
3. -1 • -10 = 10
1. x-7 is the common denominator
1. We are simplifying the numerator by combining like terms
2. The numerator is 2x+5-8x+10
1. x-7 is the common denominator

Simplify the expression shown on the right.