Calculus Examples

$\frac{(x - 3) (x - 7)}{{(x - 5)}^{2}} = 0$

Step 1

Set the numerator equal to zero.

$(x - 3) (x - 7) = 0$

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 $0$ .

$x - 3 = 0$

$x - 7 = 0$

Step 2.2

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

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Step 2.2.1

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

$x - 3 = 0$

Step 2.2.2

Add $3$ to both sides of the equation.

$x = 3$

Step 2.3

Set $x - 7$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Step 2.3.2

Add $7$ to both sides of the equation.

$x = 7$

Step 2.4

The final solution is all the values that make $(x - 3) (x - 7) = 0$ true.

$x = 3, 7$