Algebra Examples

$\frac{2 x - 8 - (x - 3)}{x^{2} - 7 x + 10}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the distributive property.

$\frac{2 x - 8 - x - - 3}{x^{2} - 7 x + 10}$

Step 1.2

Multiply $- 1$ by $- 3$ .

$\frac{2 x - 8 - x + 3}{x^{2} - 7 x + 10}$

Step 1.3

Subtract $x$ from $2 x$ .

$\frac{x - 8 + 3}{x^{2} - 7 x + 10}$

Step 1.4

Add $- 8$ and $3$ .

$\frac{x - 5}{x^{2} - 7 x + 10}$

Step 2

Factor $x^{2} - 7 x + 10$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $10$ and whose sum is $- 7$ .

$- 5, - 2$

Step 2.2

Write the factored form using these integers.

$\frac{x - 5}{(x - 5) (x - 2)}$

Step 3

Cancel the common factor of $x - 5$ .

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Step 3.1

Cancel the common factor.

$\frac{x - 5}{(x - 5) (x - 2)}$

Step 3.2

Rewrite the expression.

$\frac{1}{x - 2}$