SOLUTION: Solve the following equations and inequality for x. If the solution is extraneous, please state that it is. Please show me all work for a better understanding. 5/2x+3 = 4/x Not

Algebra ->  Inequalities -> SOLUTION: Solve the following equations and inequality for x. If the solution is extraneous, please state that it is. Please show me all work for a better understanding. 5/2x+3 = 4/x Not      Log On


   

Question 1068492: Solve the following equations and inequality for x. If the solution is extraneous, please state that it is. Please show me all work for a better understanding.
5/2x+3 = 4/x
Note: 2x+3 is the whole denominator. It is part of the first fraction and all of it is underneath the numerator.
Thank you kindly.
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
5/(2x+3)=4/x

5%2F%282x%2B3%29=4%2Fx
The simplest common denominator is x%282x%2B3%29.
Multiply BOTH SIDES of the equation by x%282x%2B3%29, simplify and solve.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F%28%282x%2B3%29%29 = 4%2Fx
Cross multiply
4(2x+3) = 5x
8x + 12 = 5x
8x - 5x = -12
3x = -12
x = -12/3
x = -4
:
Check in the original equation, will confirm it as a good solution
5%2F%28%282%28-4%29%2B3%29%29 = 4%2F%28-4%29
5%2F%28%28-8%2B3%29%29 = -1
5%2F%28-5%29 = -1
-1 = -1