Solve A-B=((2)/((3)/(sqrt(2)))-(5)/((3)/(2)))-((1)/((4)/(2sqrt(2)))-(3)/((5)/(-6))) | 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

$$A-B=( \frac{ 2 }{ \frac{ 3 }{ \sqrt{ 2 } } } - \frac{ 5 }{ \frac{ 3 }{ 2 } } )-( \frac{ 1 }{ \frac{ 4 }{ 2 \sqrt{ 2 } } } - \frac{ 3 }{ \frac{ 5 }{ -6 } } )$$

Solve for B

$B=A-\frac{\sqrt{2}}{6}+\frac{104}{15}$

Steps for Solving Linear Equation

Divide $2$ by $\frac{3}{\sqrt{2}}$ by multiplying $2$ by the reciprocal of $\frac{3}{\sqrt{2}}$.

$$A-B=\frac{2\sqrt{2}}{3}-\frac{5}{\frac{3}{2}}-\left(\frac{1}{\frac{4}{2\sqrt{2}}}-\frac{3}{\frac{5}{-6}}\right)$$

Divide $5$ by $\frac{3}{2}$ by multiplying $5$ by the reciprocal of $\frac{3}{2}$.

$$A-B=\frac{2\sqrt{2}}{3}-5\times \frac{2}{3}-\left(\frac{1}{\frac{4}{2\sqrt{2}}}-\frac{3}{\frac{5}{-6}}\right)$$

Multiply $5$ and $\frac{2}{3}$ to get $\frac{10}{3}$.

$$A-B=\frac{2\sqrt{2}}{3}-\frac{10}{3}-\left(\frac{1}{\frac{4}{2\sqrt{2}}}-\frac{3}{\frac{5}{-6}}\right)$$

Since $\frac{2\sqrt{2}}{3}$ and $\frac{10}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$A-B=\frac{2\sqrt{2}-10}{3}-\left(\frac{1}{\frac{4}{2\sqrt{2}}}-\frac{3}{\frac{5}{-6}}\right)$$

Divide $1$ by $\frac{4}{2\sqrt{2}}$ by multiplying $1$ by the reciprocal of $\frac{4}{2\sqrt{2}}$.

$$A-B=\frac{2\sqrt{2}-10}{3}-\left(\frac{2\sqrt{2}}{4}-\frac{3}{\frac{5}{-6}}\right)$$

Divide $2\sqrt{2}$ by $4$ to get $\frac{1}{2}\sqrt{2}$.

$$A-B=\frac{2\sqrt{2}-10}{3}-\left(\frac{1}{2}\sqrt{2}-\frac{3}{\frac{5}{-6}}\right)$$

Divide $3$ by $\frac{5}{-6}$ by multiplying $3$ by the reciprocal of $\frac{5}{-6}$.

$$A-B=\frac{2\sqrt{2}-10}{3}-\left(\frac{1}{2}\sqrt{2}-\frac{3\left(-6\right)}{5}\right)$$

Multiply $3$ and $-6$ to get $-18$.

$$A-B=\frac{2\sqrt{2}-10}{3}-\left(\frac{1}{2}\sqrt{2}-\frac{-18}{5}\right)$$

Fraction $\frac{-18}{5}$ can be rewritten as $-\frac{18}{5}$ by extracting the negative sign.

$$A-B=\frac{2\sqrt{2}-10}{3}-\left(\frac{1}{2}\sqrt{2}-\left(-\frac{18}{5}\right)\right)$$

The opposite of $-\frac{18}{5}$ is $\frac{18}{5}$.

$$A-B=\frac{2\sqrt{2}-10}{3}-\left(\frac{1}{2}\sqrt{2}+\frac{18}{5}\right)$$

To find the opposite of $\frac{1}{2}\sqrt{2}+\frac{18}{5}$, find the opposite of each term.

$$A-B=\frac{2\sqrt{2}-10}{3}-\frac{1}{2}\sqrt{2}-\frac{18}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3$ and $5$ is $15$. Multiply $\frac{2\sqrt{2}-10}{3}$ times $\frac{5}{5}$. Multiply $\frac{18}{5}$ times $\frac{3}{3}$.

$$A-B=\frac{5\left(2\sqrt{2}-10\right)}{15}-\frac{1}{2}\sqrt{2}-\frac{18\times 3}{15}$$

Since $\frac{5\left(2\sqrt{2}-10\right)}{15}$ and $\frac{18\times 3}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$A-B=\frac{5\left(2\sqrt{2}-10\right)-18\times 3}{15}-\frac{1}{2}\sqrt{2}$$

Do the multiplications in $5\left(2\sqrt{2}-10\right)-18\times 3$.

$$A-B=\frac{10\sqrt{2}-50-54}{15}-\frac{1}{2}\sqrt{2}$$

Do the calculations in $10\sqrt{2}-50-54$.

$$A-B=\frac{10\sqrt{2}-104}{15}-\frac{1}{2}\sqrt{2}$$

Divide each term of $10\sqrt{2}-104$ by $15$ to get $\frac{2}{3}\sqrt{2}-\frac{104}{15}$.

$$A-B=\frac{2}{3}\sqrt{2}-\frac{104}{15}-\frac{1}{2}\sqrt{2}$$

Combine $\frac{2}{3}\sqrt{2}$ and $-\frac{1}{2}\sqrt{2}$ to get $\frac{1}{6}\sqrt{2}$.

$$A-B=\frac{1}{6}\sqrt{2}-\frac{104}{15}$$

Subtract $A$ from both sides.

$$-B=\frac{1}{6}\sqrt{2}-\frac{104}{15}-A$$

The equation is in standard form.

$$-B=-A+\frac{\sqrt{2}}{6}-\frac{104}{15}$$

Divide both sides by $-1$.

$$\frac{-B}{-1}=\frac{-A+\frac{\sqrt{2}}{6}-\frac{104}{15}}{-1}$$

Dividing by $-1$ undoes the multiplication by $-1$.

$$B=\frac{-A+\frac{\sqrt{2}}{6}-\frac{104}{15}}{-1}$$

Divide $\frac{\sqrt{2}}{6}-\frac{104}{15}-A$ by $-1$.

$$B=A-\frac{\sqrt{2}}{6}+\frac{104}{15}$$

Solve for A

$A=B+\frac{\sqrt{2}}{6}-\frac{104}{15}$