What is the answer to 4/(x-1)+x=7 ?

The answer to 4/(x-1)+x=7 is x=4+sqrt(5),x=4-sqrt(5)

Solve for x: 4/(x-1)+x=7

The solution is x=4+sqrt(5),x=4-sqrt(5)

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\frac{4}{x - 1} + x = 7

x = 4 + 5, x = 4 - 5

Decimal Notation

x = 6.23606 \dots, x = 1.76393 \dots

Solution steps

\frac{4}{x - 1} + x = 7

Multiply both sides by

x - 1

4 + x (x - 1) = 7 (x - 1)

Solve

4 + x (x - 1) = 7 (x - 1) : x = 4 + 5, x = 4 - 5

x = 4 + 5, x = 4 - 5

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = 4 + 5, x = 4 - 5

\frac{5}{x + 4} - 2 = \frac{7 x + 18}{x + 4}

x - \frac{x + 5}{x + 7} = \frac{2}{x + 7}

- \frac{1}{x ^{2}} = - \frac{1}{36}

\frac{33}{b} = \frac{15}{45}

- \frac{1}{x ^{2}} = - \frac{1}{30}

What is the answer to 4/(x-1)+x=7 ?
The answer to 4/(x-1)+x=7 is x=4+sqrt(5),x=4-sqrt(5)
Solve for x: 4/(x-1)+x=7
The solution is x=4+sqrt(5),x=4-sqrt(5)