Solve (4 - (4 + a ^ 2)/a)(1/2 - 1/a) | 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

$$(4-\frac{4+a^{2}}{a})\cdot(\frac{1}{2}-\frac{1}{a})$$

Evaluate

$-\frac{\left(a-2\right)^{3}}{2a^{2}}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $4$ times $\frac{a}{a}$.

$$\left(\frac{4a}{a}-\frac{4+a^{2}}{a}\right)\left(\frac{1}{2}-\frac{1}{a}\right)$$

Since $\frac{4a}{a}$ and $\frac{4+a^{2}}{a}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a-\left(4+a^{2}\right)}{a}\left(\frac{1}{2}-\frac{1}{a}\right)$$

Do the multiplications in $4a-\left(4+a^{2}\right)$.

$$\frac{4a-4-a^{2}}{a}\left(\frac{1}{2}-\frac{1}{a}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2$ and $a$ is $2a$. Multiply $\frac{1}{2}$ times $\frac{a}{a}$. Multiply $\frac{1}{a}$ times $\frac{2}{2}$.

$$\frac{4a-4-a^{2}}{a}\left(\frac{a}{2a}-\frac{2}{2a}\right)$$

Since $\frac{a}{2a}$ and $\frac{2}{2a}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a-4-a^{2}}{a}\times \frac{a-2}{2a}$$

Multiply $\frac{4a-4-a^{2}}{a}$ times $\frac{a-2}{2a}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4a-4-a^{2}\right)\left(a-2\right)}{a\times 2a}$$

Multiply $a$ and $a$ to get $a^{2}$.

$$\frac{\left(4a-4-a^{2}\right)\left(a-2\right)}{a^{2}\times 2}$$

Use the distributive property to multiply $4a-4-a^{2}$ by $a-2$ and combine like terms.

$$\frac{6a^{2}-12a+8-a^{3}}{a^{2}\times 2}$$

Expand

$-\frac{a}{2}+3-\frac{6}{a}+\frac{4}{a^{2}}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $4$ times $\frac{a}{a}$.

$$\left(\frac{4a}{a}-\frac{4+a^{2}}{a}\right)\left(\frac{1}{2}-\frac{1}{a}\right)$$

Since $\frac{4a}{a}$ and $\frac{4+a^{2}}{a}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a-\left(4+a^{2}\right)}{a}\left(\frac{1}{2}-\frac{1}{a}\right)$$

Do the multiplications in $4a-\left(4+a^{2}\right)$.

$$\frac{4a-4-a^{2}}{a}\left(\frac{1}{2}-\frac{1}{a}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2$ and $a$ is $2a$. Multiply $\frac{1}{2}$ times $\frac{a}{a}$. Multiply $\frac{1}{a}$ times $\frac{2}{2}$.

$$\frac{4a-4-a^{2}}{a}\left(\frac{a}{2a}-\frac{2}{2a}\right)$$

Since $\frac{a}{2a}$ and $\frac{2}{2a}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a-4-a^{2}}{a}\times \frac{a-2}{2a}$$

Multiply $\frac{4a-4-a^{2}}{a}$ times $\frac{a-2}{2a}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4a-4-a^{2}\right)\left(a-2\right)}{a\times 2a}$$

Multiply $a$ and $a$ to get $a^{2}$.

$$\frac{\left(4a-4-a^{2}\right)\left(a-2\right)}{a^{2}\times 2}$$

Use the distributive property to multiply $4a-4-a^{2}$ by $a-2$ and combine like terms.

$$\frac{6a^{2}-12a+8-a^{3}}{a^{2}\times 2}$$