Algebra Examples

$\frac{5 x + 1}{5 x - 20} + \frac{x + 17}{20 - 5 x}$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Factor $5$ out of $5 x - 20$ .

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Step 1.1.1.1

Factor $5$ out of $5 x$ .

$\frac{5 x + 1}{5 (x) - 20} + \frac{x + 17}{20 - 5 x}$

Step 1.1.1.2

Factor $5$ out of $- 20$ .

$\frac{5 x + 1}{5 x + 5 \cdot - 4} + \frac{x + 17}{20 - 5 x}$

Step 1.1.1.3

Factor $5$ out of $5 x + 5 \cdot - 4$ .

$\frac{5 x + 1}{5 (x - 4)} + \frac{x + 17}{20 - 5 x}$

Step 1.1.2

Factor $5$ out of $20 - 5 x$ .

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Step 1.1.2.1

Factor $5$ out of $20$ .

$\frac{5 x + 1}{5 (x - 4)} + \frac{x + 17}{5 (4) - 5 x}$

Step 1.1.2.2

Factor $5$ out of $- 5 x$ .

$\frac{5 x + 1}{5 (x - 4)} + \frac{x + 17}{5 (4) + 5 (- x)}$

Step 1.1.2.3

Factor $5$ out of $5 (4) + 5 (- x)$ .

$\frac{5 x + 1}{5 (x - 4)} + \frac{x + 17}{5 (4 - x)}$

Step 1.2

Simplify terms.

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Step 1.2.1

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{5 x + 1}{5 (x - 4)} + \frac{x + 17}{5 (- 1 (- 4) - x)}$

Step 1.2.2

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

$\frac{5 x + 1}{5 (x - 4)} + \frac{x + 17}{5 (- 1 (- 4) - (x))}$

Step 1.2.3

Factor $- 1$ out of $- 1 (- 4) - (x)$ .

$\frac{5 x + 1}{5 (x - 4)} + \frac{x + 17}{5 (- 1 (- 4 + x))}$

Step 1.2.4

Simplify the expression.

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Step 1.2.4.1

Move a negative from the denominator of $\frac{x + 17}{5 (- 1 (- 4 + x))}$ to the numerator.

$\frac{5 x + 1}{5 (x - 4)} + \frac{- (x + 17)}{5 (- 4 + x)}$

Step 1.2.4.2

Reorder terms.

$\frac{5 x + 1}{5 (x - 4)} + \frac{- (x + 17)}{5 (x - 4)}$

Step 1.2.5

Combine the numerators over the common denominator.

$\frac{5 x + 1 - (x + 17)}{5 (x - 4)}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

$\frac{5 x + 1 - x - 1 \cdot 17}{5 (x - 4)}$

Step 2.2

Multiply $- 1$ by $17$ .

$\frac{5 x + 1 - x - 17}{5 (x - 4)}$

Step 2.3

Subtract $x$ from $5 x$ .

$\frac{4 x + 1 - 17}{5 (x - 4)}$

Step 2.4

Subtract $17$ from $1$ .

$\frac{4 x - 16}{5 (x - 4)}$

Step 2.5

Factor $4$ out of $4 x - 16$ .

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Step 2.5.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 16}{5 (x - 4)}$

Step 2.5.2

Factor $4$ out of $- 16$ .

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

Step 2.5.3

Factor $4$ out of $4 x + 4 \cdot - 4$ .

$\frac{4 (x - 4)}{5 (x - 4)}$

Step 3

Cancel the common factor of $x - 4$ .

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Step 3.1

Cancel the common factor.

$\frac{4 (x - 4)}{5 (x - 4)}$

Step 3.2

Rewrite the expression.

$\frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$