How do you solve 4 /(x+1 )+ 3 /(x - 4) = 2 /( x +1)?

2 Answers
Apr 17, 2018

x=1

Explanation:

Assuming you want to solve for x, find the common denominator for the left side, (x+1)(x-4) and combine them into a single rational equation. Since 4/(x+1) and 3/(x-4) combine, it turns into (7x-13)/((x+1)(x-4)) by multiplying the numerator 4*(x-4) and 3*(x+1), adding them and combining like terms . You want to get rid of any denominators in the problem to make it simpler, so multiply that common denominator to both sides of the equation,
(7x-13)/((x+1)(x-4))*(x+1)(x+4) and same with the right side. On the left the common denominator gets cancelled so you're left with 7x-13. On the right the (x+1) gets cancelled and you have 2(x-4). Multiply that and overall you have 7x-13=2x-8 left. then bring the x's on one side and the rest on the other side. 7x-2x=-8+13 , add and finally you have, 5x=5, x=1. To check you can plug x in the original equation.

Apr 17, 2018

x=1

Explanation:

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

Our strategy will be to eliminate quotients.

This equation will look a lot less scary if we multiply both sides by x+1.

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

Now subtract 4 from both sides of the equation.

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

Now multiply both side s of the equation by x-4.

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

Hey! No more quotients! Now apply the distributive property.

3x+3=-2x+8

Add 2x to both sides of this equation.

5x+3=8

Subtract 3 from both sides of this equation.

5x=5

Divide both sides of this equation by 5.

x=1

We can check our answer.

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

4/2+3/-3 =?= 2/2

2-1 =?= 1

1=1

Wadya know? Algebra WORKS!