# (2x+3)/(x+2)=3/2Math problem; solve the following rational equation

Luca B. | Certified Educator

calendarEducator since 2011

starTop subjects are Math, Science, and Business

You need to have all terms to the left side.

Subtracting 3/2 both sides yields:

`(2x+3)/(x+2) - 3/2 = 0`

You need to bring both fractions to a common denominator such that:

`(2(2x+3) - 3(x+2))/(2(x+2)) = 0`

Opening the brackets yields:

`(4x + 6 - 3x - 6)/(2(x+2)) = 0`

`` `x/(2(x+2)) = 0`

The denominator of the fraction must not be zero => `x+2 != 0`  => `x != -2` .

If the fraction yields 0 => x = 0.

The solution to the given equation is x = 0.

check Approved by eNotes Editorial

kclaibourn | Student
(2x+3)/(x+2) = 3/2 1. (x+2)[(2x+3)/(x+2)] = 3/2(x+2) multiply both sides by (x+2) 2. (2x+3)=3/2x + 3 multiply using distibutive property 3. (2x+3)-3/2x = (3/2x+3)-3/2x subract 3/2x from both sides 3. (1/2x+3)-3 = (3)- 3 subtract 3 from both sides 4. (1/2x)/ 1/2 = 0 / 1/2 divide both sides by 1/2 5. x = 0