Solving Rational equations that lead to linear equations

Question

((4x+3)/4)-(2x/(x+1))=x

Answer 1

We find the LCD of the equation.  LCD is  4(x + 1).

 

 

[(x + 1)(4x + 3) - 8x] / (4(x + 1) = [4x(x + 1)] / (4(x + 1))

 

 

Equate numerators.

 

(x + 1)(4x + 3) - 8x = 4x(x + 1)

 

 

Now we distribute to get rid of parentheses.

 

4x² + 7x + 3 - 8x = 4x² + 4x

 

4x² - x + 3 = 4x² + 4x

 

 

Subtract 4x² on both sides of the equation.

 

-x + 3 = 4x         ------>       linear equation

 

 

Add x on both sides of the equation.

 

3 = 5x

 

 

Divide both sides of the equation by 5.

 

3 / 5 = x

Answer 2

(4x+3)/4 - 2x/(x+1) = x

 

Multiply the equation by 4(x+1):  (x+1)(4x+3) - 8x = 4x(x+1)

 

                       Simplify to get:  4x²+7x+3-8x = 4x²+4x

 

                                                           3-x = 4x

 

                                                             5x = 3

 

                                                               x = 3/5