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

Answer 1

#x# = #1#.

First, multiply and divide the first fraction on the left by #x-4# and the second fraction on the left by #x+1# to make them comparable.
We get #(4(x-4) + 3(x+1))/((x+1)(x-4))# = #2/(x+1)#.
After cancelling #x+1# on both sides, we get,
#(4(x-4) + 3(x+1))/(x-4)# = #2#.

After cross-multiplying the denominator and expanding the numerator, we obtain

#7x-13# = #2x-8#
This gives us #5x# = #5#
And thus #x# = #1#.
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Answer 2

To solve the equation 4 / (x+1) + 3 /( x - 4) = 2 /( x +1), we can start by finding a common denominator for all the fractions. The common denominator in this case is (x+1)(x-4).

Multiplying each term by the common denominator, we get: 4(x-4) + 3(x+1) = 2(x-4)

Expanding and simplifying the equation, we have: 4x - 16 + 3x + 3 = 2x - 8

Combining like terms, we get: 7x - 13 = 2x - 8

Moving all the x terms to one side and the constant terms to the other side, we have: 7x - 2x = -8 + 13

Simplifying further, we get: 5x = 5

Dividing both sides by 5, we find: x = 1

Therefore, the solution to the equation 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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