Simplify (x-2)/(4x)+(x+5)/(10x)

$\frac{x - 2}{4 x} + \frac{x + 5}{10 x}$

Step 1

To write $\frac{x - 2}{4 x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x - 2}{4 x} \cdot \frac{5}{5} + \frac{x + 5}{10 x}$

Step 2

To write $\frac{x + 5}{10 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x - 2}{4 x} \cdot \frac{5}{5} + \frac{x + 5}{10 x} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $20 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x - 2}{4 x}$ by $\frac{5}{5}$ .

$\frac{(x - 2) \cdot 5}{4 x \cdot 5} + \frac{x + 5}{10 x} \cdot \frac{2}{2}$

Multiply $5$ by $4$ .

$\frac{(x - 2) \cdot 5}{20 x} + \frac{x + 5}{10 x} \cdot \frac{2}{2}$

Multiply $\frac{x + 5}{10 x}$ by $\frac{2}{2}$ .

$\frac{(x - 2) \cdot 5}{20 x} + \frac{(x + 5) \cdot 2}{10 x \cdot 2}$

Multiply $2$ by $10$ .

$\frac{(x - 2) \cdot 5}{20 x} + \frac{(x + 5) \cdot 2}{20 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{(x - 2) \cdot 5 + (x + 5) \cdot 2}{20 x}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 5 - 2 \cdot 5 + (x + 5) \cdot 2}{20 x}$

Move $5$ to the left of $x$ .

$\frac{5 \cdot x - 2 \cdot 5 + (x + 5) \cdot 2}{20 x}$

Multiply $- 2$ by $5$ .

$\frac{5 \cdot x - 10 + (x + 5) \cdot 2}{20 x}$

Apply the distributive property.

$\frac{5 x - 10 + x \cdot 2 + 5 \cdot 2}{20 x}$

Move $2$ to the left of $x$ .

$\frac{5 x - 10 + 2 \cdot x + 5 \cdot 2}{20 x}$

Multiply $5$ by $2$ .

$\frac{5 x - 10 + 2 \cdot x + 10}{20 x}$

Add $5 x$ and $2 x$ .

$\frac{7 x - 10 + 10}{20 x}$

Add $- 10$ and $10$ .

$\frac{7 x + 0}{20 x}$

Add $7 x$ and $0$ .

$\frac{7 x}{20 x}$

Step 6

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{7 x}{20 x}$

Rewrite the expression.

$\frac{7}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{20}$

Decimal Form:

$0.35$

Simplify (x-2)/(4x)+(x+5)/(10x)

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