Simplify x/2+(x^2)/3-x/5-(x^2)/4

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

Step 1

Find the common denominator.

Multiply $\frac{x}{2}$ by $\frac{30}{30}$ .

$\frac{x}{2} \cdot \frac{30}{30} + \frac{x^{2}}{3} - \frac{x}{5} - \frac{x^{2}}{4}$

Multiply $\frac{x}{2}$ by $\frac{30}{30}$ .

$\frac{x \cdot 30}{2 \cdot 30} + \frac{x^{2}}{3} - \frac{x}{5} - \frac{x^{2}}{4}$

Multiply $\frac{x^{2}}{3}$ by $\frac{20}{20}$ .

$\frac{x \cdot 30}{2 \cdot 30} + \frac{x^{2}}{3} \cdot \frac{20}{20} - \frac{x}{5} - \frac{x^{2}}{4}$

Multiply $\frac{x^{2}}{3}$ by $\frac{20}{20}$ .

$\frac{x \cdot 30}{2 \cdot 30} + \frac{x^{2} \cdot 20}{3 \cdot 20} - \frac{x}{5} - \frac{x^{2}}{4}$

Multiply $\frac{x}{5}$ by $\frac{12}{12}$ .

$\frac{x \cdot 30}{2 \cdot 30} + \frac{x^{2} \cdot 20}{3 \cdot 20} - (\frac{x}{5} \cdot \frac{12}{12}) - \frac{x^{2}}{4}$

Multiply $\frac{x}{5}$ by $\frac{12}{12}$ .

$\frac{x \cdot 30}{2 \cdot 30} + \frac{x^{2} \cdot 20}{3 \cdot 20} - \frac{x \cdot 12}{5 \cdot 12} - \frac{x^{2}}{4}$

Multiply $\frac{x^{2}}{4}$ by $\frac{15}{15}$ .

$\frac{x \cdot 30}{2 \cdot 30} + \frac{x^{2} \cdot 20}{3 \cdot 20} - \frac{x \cdot 12}{5 \cdot 12} - (\frac{x^{2}}{4} \cdot \frac{15}{15})$

Multiply $\frac{x^{2}}{4}$ by $\frac{15}{15}$ .

$\frac{x \cdot 30}{2 \cdot 30} + \frac{x^{2} \cdot 20}{3 \cdot 20} - \frac{x \cdot 12}{5 \cdot 12} - \frac{x^{2} \cdot 15}{4 \cdot 15}$

Multiply $2$ by $30$ .

$\frac{x \cdot 30}{60} + \frac{x^{2} \cdot 20}{3 \cdot 20} - \frac{x \cdot 12}{5 \cdot 12} - \frac{x^{2} \cdot 15}{4 \cdot 15}$

Multiply $3$ by $20$ .

$\frac{x \cdot 30}{60} + \frac{x^{2} \cdot 20}{60} - \frac{x \cdot 12}{5 \cdot 12} - \frac{x^{2} \cdot 15}{4 \cdot 15}$

Multiply $5$ by $12$ .

$\frac{x \cdot 30}{60} + \frac{x^{2} \cdot 20}{60} - \frac{x \cdot 12}{60} - \frac{x^{2} \cdot 15}{4 \cdot 15}$

Multiply $4$ by $15$ .

$\frac{x \cdot 30}{60} + \frac{x^{2} \cdot 20}{60} - \frac{x \cdot 12}{60} - \frac{x^{2} \cdot 15}{60}$

Step 2

Combine the numerators over the common denominator.

$\frac{x \cdot 30 + x^{2} \cdot 20 - x \cdot 12 - x^{2} \cdot 15}{60}$

Step 3

Simplify each term.

Move $30$ to the left of $x$ .

$\frac{30 \cdot x + x^{2} \cdot 20 - x \cdot 12 - x^{2} \cdot 15}{60}$

Move $20$ to the left of $x^{2}$ .

$\frac{30 x + 20 \cdot x^{2} - x \cdot 12 - x^{2} \cdot 15}{60}$

Multiply $12$ by $- 1$ .

$\frac{30 x + 20 x^{2} - 12 x - x^{2} \cdot 15}{60}$

Multiply $15$ by $- 1$ .

$\frac{30 x + 20 x^{2} - 12 x - 15 x^{2}}{60}$

Step 4

Simplify terms.

Subtract $12 x$ from $30 x$ .

$\frac{20 x^{2} + 18 x - 15 x^{2}}{60}$

Subtract $15 x^{2}$ from $20 x^{2}$ .

$\frac{5 x^{2} + 18 x}{60}$

Factor $x$ out of $5 x^{2} + 18 x$ .

Factor $x$ out of $5 x^{2}$ .

$\frac{x (5 x) + 18 x}{60}$

Factor $x$ out of $18 x$ .

$\frac{x (5 x) + x \cdot 18}{60}$

Factor $x$ out of $x (5 x) + x \cdot 18$ .

$\frac{x (5 x + 18)}{60}$

Simplify x/2+(x^2)/3-x/5-(x^2)/4

Related Questions

Support LCMGCF.com by disabling your adblocker.