Question

Solve for x
$\sf \dfrac{3x + 4}{x - 1} = 2+\dfrac{7}{x -1}$

Answer 1

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Answer 2

Step-by-step explanation:

Given:-

(3x+4)/(x-1) = 2+[7/(x-1)]

To find:-

Find the value of x for the given problem?

Solution:-

Given equation is (3x+4)/(x-1) = 2+[7/(x-1)]

=>(3x+4)/(x-1) = [2(x-1)+7]/(x-1)

=>(3x+4)/(x-1) = [2x-2+7]/(x-1)

=>(3x+4)/(x-1) = (2x+5)/(x-1)

On cancelling (x-1) both sides then

=>3x+4 = 2x+5

=>3x - 2x = 5 - 4

=>x = 1

Therefore, x= 1

Answer:-

The value of x for the given problem is 1

Check:-

If x= 1 then LHS:-

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

=>(3×1+4)/(1-1)

=>(3+5)/0

=>8/0

=>not defined

RHS:-

2+[7/(x-1)]

=>2+(7/(1-1)

=>2+7/0

=> not defined

LHS = RHS is true for x=1