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

Answer 1

#x=1#

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.
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Answer 2

#x=1#

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

Our plan is to get rid of 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 take 4 out of the equation on both sides.

#(3(x+1))/(x-4)=-2#
Now multiply both side s of the equation by #x-4#.
#3(x+1)=-2(x-4)#

Apply the distributive property now, and let's stop using quotients.

#3x+3=-2x+8#
Add #2x# to both sides of this equation.
#5x+3=8#

From both sides of this equation, subtract 3.

#5x=5#

This equation's two sides should be divided by 5.

#x=1#

We can verify our response.

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

You know what? Algebra WORKS!

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Answer 3

To solve the equation 4/(x+1) + 3/(x-4) = 2/(x+1), we can follow these steps:

  1. Multiply the entire equation by the common denominator, which is (x+1)(x-4). This will eliminate the denominators.

(x+1)(x-4) * [4/(x+1) + 3/(x-4)] = (x+1)(x-4) * 2/(x+1)

  1. Simplify the equation by distributing and canceling out common factors:

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

  1. Expand and simplify the equation:

4x - 16 + 3x + 3 = 2x - 8

7x - 13 = 2x - 8

  1. Move all the variables to one side and the constants to the other side:

7x - 2x = -8 + 13

5x = 5

  1. Solve for x by dividing both sides of the equation by 5:

x = 1

Therefore, the solution to the equation 4/(x+1) + 3/(x-4) = 2/(x+1) is x = 1.

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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.

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.

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.

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.

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