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

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

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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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