Solve ((7(x)^(2))/(2)-11x)/(((x)^(3))/(3)-(3(x)^(2))/(2)+2x) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{ \frac{ 7 { x }^{ 2 } }{ 2 } -11x }{ \frac{ { x }^{ 3 } }{ 3 } - \frac{ 3 { x }^{ 2 } }{ 2 } +2x }$$

Evaluate

$\frac{3\left(7x-22\right)}{2x^{2}-9x+12}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $-11x$ times $\frac{2}{2}$.

$$\frac{\frac{7x^{2}}{2}+\frac{2\left(-11\right)x}{2}}{\frac{x^{3}}{3}-\frac{3x^{2}}{2}+2x}$$

Since $\frac{7x^{2}}{2}$ and $\frac{2\left(-11\right)x}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{7x^{2}+2\left(-11\right)x}{2}}{\frac{x^{3}}{3}-\frac{3x^{2}}{2}+2x}$$

Do the multiplications in $7x^{2}+2\left(-11\right)x$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{x^{3}}{3}-\frac{3x^{2}}{2}+2x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3$ and $2$ is $6$. Multiply $\frac{x^{3}}{3}$ times $\frac{2}{2}$. Multiply $\frac{3x^{2}}{2}$ times $\frac{3}{3}$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}}{6}-\frac{3\times 3x^{2}}{6}+2x}$$

Since $\frac{2x^{3}}{6}$ and $\frac{3\times 3x^{2}}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-3\times 3x^{2}}{6}+2x}$$

Do the multiplications in $2x^{3}-3\times 3x^{2}$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-9x^{2}}{6}+2x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $2x$ times $\frac{6}{6}$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-9x^{2}}{6}+\frac{6\times 2x}{6}}$$

Since $\frac{2x^{3}-9x^{2}}{6}$ and $\frac{6\times 2x}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-9x^{2}+6\times 2x}{6}}$$

Do the multiplications in $2x^{3}-9x^{2}+6\times 2x$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-9x^{2}+12x}{6}}$$

Divide $\frac{7x^{2}-22x}{2}$ by $\frac{2x^{3}-9x^{2}+12x}{6}$ by multiplying $\frac{7x^{2}-22x}{2}$ by the reciprocal of $\frac{2x^{3}-9x^{2}+12x}{6}$.

$$\frac{\left(7x^{2}-22x\right)\times 6}{2\left(2x^{3}-9x^{2}+12x\right)}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{3\left(7x^{2}-22x\right)}{2x^{3}-9x^{2}+12x}$$

Factor the expressions that are not already factored.

$$\frac{3x\left(7x-22\right)}{x\left(2x^{2}-9x+12\right)}$$

Cancel out $x$ in both numerator and denominator.

$$\frac{3\left(7x-22\right)}{2x^{2}-9x+12}$$

Expand the expression.

$$\frac{21x-66}{2x^{2}-9x+12}$$

Expand

$\frac{3\left(7x-22\right)}{2x^{2}-9x+12}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $-11x$ times $\frac{2}{2}$.

$$\frac{\frac{7x^{2}}{2}+\frac{2\left(-11\right)x}{2}}{\frac{x^{3}}{3}-\frac{3x^{2}}{2}+2x}$$

Since $\frac{7x^{2}}{2}$ and $\frac{2\left(-11\right)x}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{7x^{2}+2\left(-11\right)x}{2}}{\frac{x^{3}}{3}-\frac{3x^{2}}{2}+2x}$$

Do the multiplications in $7x^{2}+2\left(-11\right)x$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{x^{3}}{3}-\frac{3x^{2}}{2}+2x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3$ and $2$ is $6$. Multiply $\frac{x^{3}}{3}$ times $\frac{2}{2}$. Multiply $\frac{3x^{2}}{2}$ times $\frac{3}{3}$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}}{6}-\frac{3\times 3x^{2}}{6}+2x}$$

Since $\frac{2x^{3}}{6}$ and $\frac{3\times 3x^{2}}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-3\times 3x^{2}}{6}+2x}$$

Do the multiplications in $2x^{3}-3\times 3x^{2}$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-9x^{2}}{6}+2x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $2x$ times $\frac{6}{6}$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-9x^{2}}{6}+\frac{6\times 2x}{6}}$$

Since $\frac{2x^{3}-9x^{2}}{6}$ and $\frac{6\times 2x}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-9x^{2}+6\times 2x}{6}}$$

Do the multiplications in $2x^{3}-9x^{2}+6\times 2x$.

$$\frac{\frac{7x^{2}-22x}{2}}{\frac{2x^{3}-9x^{2}+12x}{6}}$$

Divide $\frac{7x^{2}-22x}{2}$ by $\frac{2x^{3}-9x^{2}+12x}{6}$ by multiplying $\frac{7x^{2}-22x}{2}$ by the reciprocal of $\frac{2x^{3}-9x^{2}+12x}{6}$.

$$\frac{\left(7x^{2}-22x\right)\times 6}{2\left(2x^{3}-9x^{2}+12x\right)}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{3\left(7x^{2}-22x\right)}{2x^{3}-9x^{2}+12x}$$

Factor the expressions that are not already factored.

$$\frac{3x\left(7x-22\right)}{x\left(2x^{2}-9x+12\right)}$$

Cancel out $x$ in both numerator and denominator.

$$\frac{3\left(7x-22\right)}{2x^{2}-9x+12}$$

Expand the expression.

$$\frac{21x-66}{2x^{2}-9x+12}$$