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 $6$ .

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

Step 1.1.3

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

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

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

Add $16$ and $3$ .

$\frac{- 5}{2 (x^{2} - 8 x + 19)}$

Step 2

Move the negative in front of the fraction.

$- \frac{5}{2 (x^{2} - 8 x + 19)}$