Algebra Examples

$\frac{(x - 5) (x - 1) (3 + x)}{7 x - 7} = 0$

Step 1

Set the numerator equal to zero.

$(x - 5) (x - 1) (3 + x) = 0$

Step 2

Solve the equation for $x$ .

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Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 5 = 0$

$x - 1 = 0$

$3 + x = 0$

Step 2.2

Set $x - 5$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Step 2.2.2

Add $5$ to both sides of the equation.

$x = 5$

Step 2.3

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 2.3.2

Add $1$ to both sides of the equation.

$x = 1$

Step 2.4

Set $3 + x$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $3 + x$ equal to $0$ .

$3 + x = 0$

Step 2.4.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 2.5

The final solution is all the values that make $(x - 5) (x - 1) (3 + x) = 0$ true.

$x = 5, 1, - 3$

Step 3

Exclude the solutions that do not make $\frac{(x - 5) (x - 1) (3 + x)}{7 x - 7} = 0$ true.

$x = 5, - 3$

Step 4