Check the solution to "Solve the equation 2+5x−4=x+1x−4"

banganX

Answered question

2021-09-15

Solve the equation

2 + \frac{5}{x - 4} = \frac{x + 1}{x - 4}

Nicole Conner

Skilled2021-09-16Added 97 answers

Step 1
Given equation:

2 + \frac{5}{x - 4} = \frac{x + 1}{x - 4}

Solving for x:=?

2 + \frac{5}{x - 4} = \frac{x + 1}{x - 4}

Using the property of fractions:
We just need to evaluate this fraction by taking the L.C.M on the left hand side of this expression:
Step 2
Hence:

2 + \frac{5}{x - 4} = \frac{x + 1}{x - 4}

\frac{2 (x - 4) + 5}{x - 4} = \frac{x + 1}{x - 4}

\frac{2 x - 8 + 5}{x - 4} = \frac{x + 1}{x - 4}

\frac{2 x - 3}{x - 4} = \frac{x + 1}{x - 4}

Cancelling out the same denominators:
We get:

2 x - 3 = x + 1

2 x - x = 1 + 3

x = 4

;
Hence,
The solution for the given expression is 4;

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