Solve (-(1)/(2)+(3)/(4)-(5)/(3)+(3)/(2))((1)/(2)-(3)/(4)-(5)/(3)+(3)/(2))= | 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

$$(- \frac{ 1 }{ 2 } + \frac{ 3 }{ 4 } - \frac{ 5 }{ 3 } + \frac{ 3 }{ 2 } )( \frac{ 1 }{ 2 } - \frac{ 3 }{ 4 } - \frac{ 5 }{ 3 } + \frac{ 3 }{ 2 } )=$$

Evaluate

$-\frac{5}{144}\approx -0.034722222$

Solution Steps

Least common multiple of $2$ and $4$ is $4$. Convert $-\frac{1}{2}$ and $\frac{3}{4}$ to fractions with denominator $4$.

$$\left(-\frac{2}{4}+\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)\left(\frac{1}{2}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Since $-\frac{2}{4}$ and $\frac{3}{4}$ have the same denominator, add them by adding their numerators.

$$\left(\frac{-2+3}{4}-\frac{5}{3}+\frac{3}{2}\right)\left(\frac{1}{2}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Add $-2$ and $3$ to get $1$.

$$\left(\frac{1}{4}-\frac{5}{3}+\frac{3}{2}\right)\left(\frac{1}{2}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Least common multiple of $4$ and $3$ is $12$. Convert $\frac{1}{4}$ and $\frac{5}{3}$ to fractions with denominator $12$.

$$\left(\frac{3}{12}-\frac{20}{12}+\frac{3}{2}\right)\left(\frac{1}{2}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Since $\frac{3}{12}$ and $\frac{20}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3-20}{12}+\frac{3}{2}\right)\left(\frac{1}{2}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Subtract $20$ from $3$ to get $-17$.

$$\left(-\frac{17}{12}+\frac{3}{2}\right)\left(\frac{1}{2}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Least common multiple of $12$ and $2$ is $12$. Convert $-\frac{17}{12}$ and $\frac{3}{2}$ to fractions with denominator $12$.

$$\left(-\frac{17}{12}+\frac{18}{12}\right)\left(\frac{1}{2}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Since $-\frac{17}{12}$ and $\frac{18}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{-17+18}{12}\left(\frac{1}{2}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Add $-17$ and $18$ to get $1$.

$$\frac{1}{12}\left(\frac{1}{2}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Least common multiple of $2$ and $4$ is $4$. Convert $\frac{1}{2}$ and $\frac{3}{4}$ to fractions with denominator $4$.

$$\frac{1}{12}\left(\frac{2}{4}-\frac{3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Since $\frac{2}{4}$ and $\frac{3}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{12}\left(\frac{2-3}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Subtract $3$ from $2$ to get $-1$.

$$\frac{1}{12}\left(-\frac{1}{4}-\frac{5}{3}+\frac{3}{2}\right)$$

Least common multiple of $4$ and $3$ is $12$. Convert $-\frac{1}{4}$ and $\frac{5}{3}$ to fractions with denominator $12$.

$$\frac{1}{12}\left(-\frac{3}{12}-\frac{20}{12}+\frac{3}{2}\right)$$

Since $-\frac{3}{12}$ and $\frac{20}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{12}\left(\frac{-3-20}{12}+\frac{3}{2}\right)$$

Subtract $20$ from $-3$ to get $-23$.

$$\frac{1}{12}\left(-\frac{23}{12}+\frac{3}{2}\right)$$

Least common multiple of $12$ and $2$ is $12$. Convert $-\frac{23}{12}$ and $\frac{3}{2}$ to fractions with denominator $12$.

$$\frac{1}{12}\left(-\frac{23}{12}+\frac{18}{12}\right)$$

Since $-\frac{23}{12}$ and $\frac{18}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{1}{12}\times \frac{-23+18}{12}$$

Add $-23$ and $18$ to get $-5$.

$$\frac{1}{12}\left(-\frac{5}{12}\right)$$

Multiply $\frac{1}{12}$ times $-\frac{5}{12}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-5\right)}{12\times 12}$$

Do the multiplications in the fraction $\frac{1\left(-5\right)}{12\times 12}$.

$$\frac{-5}{144}$$

Fraction $\frac{-5}{144}$ can be rewritten as $-\frac{5}{144}$ by extracting the negative sign.

$$-\frac{5}{144}$$

Factor

$-\frac{5}{144} = -0.034722222222222224$