Home > Algebra > Multiplication of Rational Expressions

What is the sum of #\frac { - x + 7} { 2x + 4}# and #\frac { 2x + 5} { 2x + 4} #?

Answer 1

Avery Alexander

See the solution process below:

We can rewrite this as the expression:

#(-x + 7)/(2x + 4) + (2x + 5)/(2x + 4)#

Because both terms have the same denominator we can add the numerators over the common denominator:

#((-x + 7) + (2x + 5))/(2x + 4)#

We can now group and combine like terms in the numerator:

#(-x + 7+ 2x + 5)/(2x + 4)#

#(2x - x + 7 + 5)/(2x + 4)#

#(2x - 1x + 7 + 5)/(2x + 4)#

#((2 - 1)x + (7 + 5))/(2x + 4)#

#(1x + 12)/(2x + 4)#

#(x + 12)/(2x + 4)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.