Algebra Examples

$\frac{5}{- 2 {(x - 4)}^{2} + 6}$

Step 1

Simplify the denominator.

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Step 1.1

Factor $2$ out of $- 2 {(x - 4)}^{2} + 6$ .

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Step 1.1.1

Factor $2$ out of $- 2 {(x - 4)}^{2}$ .

$\frac{5}{2 (- {(x - 4)}^{2}) + 6}$

Step 1.1.2

Factor $2$ out of $6$ .

$\frac{5}{2 (- {(x - 4)}^{2}) + 2 (3)}$

Step 1.1.3

Factor $2$ out of $2 (- {(x - 4)}^{2}) + 2 (3)$ .

$\frac{5}{2 (- {(x - 4)}^{2} + 3)}$

Step 1.2

Rewrite ${(x - 4)}^{2}$ as $(x - 4) (x - 4)$ .

$\frac{5}{2 (- ((x - 4) (x - 4)) + 3)}$

Step 1.3

Expand $(x - 4) (x - 4)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$\frac{5}{2 (- (x (x - 4) - 4 (x - 4)) + 3)}$

Step 1.3.2

Apply the distributive property.

$\frac{5}{2 (- (x \cdot x + x \cdot - 4 - 4 (x - 4)) + 3)}$

Step 1.3.3

Apply the distributive property.

$\frac{5}{2 (- (x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4) + 3)}$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

$\frac{5}{2 (- (x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4) + 3)}$

Step 1.4.1.2

Move $- 4$ to the left of $x$ .

$\frac{5}{2 (- (x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4) + 3)}$

Step 1.4.1.3

Multiply $- 4$ by $- 4$ .

$\frac{5}{2 (- (x^{2} - 4 x - 4 x + 16) + 3)}$

Step 1.4.2

Subtract $4 x$ from $- 4 x$ .

$\frac{5}{2 (- (x^{2} - 8 x + 16) + 3)}$

Step 1.5

Apply the distributive property.

$\frac{5}{2 (- x^{2} - (- 8 x) - 1 \cdot 16 + 3)}$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $- 8$ by $- 1$ .

$\frac{5}{2 (- x^{2} + 8 x - 1 \cdot 16 + 3)}$

Step 1.6.2

Multiply $- 1$ by $16$ .

$\frac{5}{2 (- x^{2} + 8 x - 16 + 3)}$

Step 1.7

Add $- 16$ and $3$ .

$\frac{5}{2 (- x^{2} + 8 x - 13)}$

Step 2

Simplify with factoring out.

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Step 2.1

Factor $- 1$ out of $- x^{2}$ .

$\frac{5}{2 (- (x^{2}) + 8 x - 13)}$

Step 2.2

Factor $- 1$ out of $8 x$ .

$\frac{5}{2 (- (x^{2}) - (- 8 x) - 13)}$

Step 2.3

Factor $- 1$ out of $- (x^{2}) - (- 8 x)$ .

$\frac{5}{2 (- (x^{2} - 8 x) - 13)}$

Step 2.4

Rewrite $- 13$ as $- 1 (13)$ .

$\frac{5}{2 (- (x^{2} - 8 x) - 1 (13))}$

Step 2.5

Factor $- 1$ out of $- (x^{2} - 8 x) - 1 (13)$ .

$\frac{5}{2 (- (x^{2} - 8 x + 13))}$

Step 2.6

Rewrite negatives.

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Step 2.6.1

Rewrite $- (x^{2} - 8 x + 13)$ as $- 1 (x^{2} - 8 x + 13)$ .

$\frac{5}{2 (- 1 (x^{2} - 8 x + 13))}$

Step 2.6.2

Move the negative in front of the fraction.

$- \frac{5}{2 (x^{2} - 8 x + 13)}$