Solve (5\times-(51)/(73))/(3)-((-(51)/(73)-1))/(4)=(-(51)/(73)-3)/(5) | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

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Question

$$\frac{ 5 \times - \frac{ 51 }{ 73 } }{ 3 } - \frac{ (- \frac{ 51 }{ 73 } -1) }{ 4 } = \frac{ - \frac{ 51 }{ 73 } -3 }{ 5 }$$

Verify

$\text{true}$

Solution Steps

Multiply both sides of the equation by $60$, the least common multiple of $3,4,5$.

$$20\times 5\left(-\frac{51}{73}\right)-15\left(-\frac{51}{73}-1\right)=12\left(-\frac{51}{73}-3\right)$$

Multiply $20$ and $5$ to get $100$.

$$100\left(-\frac{51}{73}\right)-15\left(-\frac{51}{73}-1\right)=12\left(-\frac{51}{73}-3\right)$$

Express $100\left(-\frac{51}{73}\right)$ as a single fraction.

$$\frac{100\left(-51\right)}{73}-15\left(-\frac{51}{73}-1\right)=12\left(-\frac{51}{73}-3\right)$$

Multiply $100$ and $-51$ to get $-5100$.

$$\frac{-5100}{73}-15\left(-\frac{51}{73}-1\right)=12\left(-\frac{51}{73}-3\right)$$

Fraction $\frac{-5100}{73}$ can be rewritten as $-\frac{5100}{73}$ by extracting the negative sign.

$$-\frac{5100}{73}-15\left(-\frac{51}{73}-1\right)=12\left(-\frac{51}{73}-3\right)$$

Convert $1$ to fraction $\frac{73}{73}$.

$$-\frac{5100}{73}-15\left(-\frac{51}{73}-\frac{73}{73}\right)=12\left(-\frac{51}{73}-3\right)$$

Since $-\frac{51}{73}$ and $\frac{73}{73}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5100}{73}-15\times \frac{-51-73}{73}=12\left(-\frac{51}{73}-3\right)$$

Subtract $73$ from $-51$ to get $-124$.

$$-\frac{5100}{73}-15\left(-\frac{124}{73}\right)=12\left(-\frac{51}{73}-3\right)$$

Express $-15\left(-\frac{124}{73}\right)$ as a single fraction.

$$-\frac{5100}{73}+\frac{-15\left(-124\right)}{73}=12\left(-\frac{51}{73}-3\right)$$

Multiply $-15$ and $-124$ to get $1860$.

$$-\frac{5100}{73}+\frac{1860}{73}=12\left(-\frac{51}{73}-3\right)$$

Since $-\frac{5100}{73}$ and $\frac{1860}{73}$ have the same denominator, add them by adding their numerators.

$$\frac{-5100+1860}{73}=12\left(-\frac{51}{73}-3\right)$$

Add $-5100$ and $1860$ to get $-3240$.

$$-\frac{3240}{73}=12\left(-\frac{51}{73}-3\right)$$

Convert $3$ to fraction $\frac{219}{73}$.

$$-\frac{3240}{73}=12\left(-\frac{51}{73}-\frac{219}{73}\right)$$

Since $-\frac{51}{73}$ and $\frac{219}{73}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3240}{73}=12\times \frac{-51-219}{73}$$

Subtract $219$ from $-51$ to get $-270$.

$$-\frac{3240}{73}=12\left(-\frac{270}{73}\right)$$

Express $12\left(-\frac{270}{73}\right)$ as a single fraction.

$$-\frac{3240}{73}=\frac{12\left(-270\right)}{73}$$

Multiply $12$ and $-270$ to get $-3240$.

$$-\frac{3240}{73}=\frac{-3240}{73}$$

Fraction $\frac{-3240}{73}$ can be rewritten as $-\frac{3240}{73}$ by extracting the negative sign.

$$-\frac{3240}{73}=-\frac{3240}{73}$$

Compare $-\frac{3240}{73}$ and $-\frac{3240}{73}$.

$$\text{true}$$