Solve frac{{[5^2-6*(-5)]:(-11)+3*(7-11)}*(-3)-2}{{[25-6*(-5)]:(-11)+21-32}*(-3)-2}

$$\frac { \{ [ 5 ^ { 2 } - 6 \cdot ( - 5 ) ] : ( - 11 ) + 3 \cdot ( 7 - 11 ) \} \cdot ( - 3 ) - 2 } { \{ [ 25 - 6 \cdot ( - 5 ) ] : ( - 11 ) + 21 - 32 \} \cdot ( - 3 ) - 2 }$$

Evaluate

$$\frac{49}{46}\approx 1.065217391$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{\left(\frac{25-6\left(-5\right)}{-11}+3\left(7-11\right)\right)\left(-3\right)-2}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

Multiply 6 and -5 to get -30.

$$\frac{\left(\frac{25-\left(-30\right)}{-11}+3\left(7-11\right)\right)\left(-3\right)-2}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

The opposite of -30 is 30.

$$\frac{\left(\frac{25+30}{-11}+3\left(7-11\right)\right)\left(-3\right)-2}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

Add 25 and 30 to get 55.

$$\frac{\left(\frac{55}{-11}+3\left(7-11\right)\right)\left(-3\right)-2}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

Divide 55 by -11 to get -5.

$$\frac{\left(-5+3\left(7-11\right)\right)\left(-3\right)-2}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

Subtract 11 from 7 to get -4.

$$\frac{\left(-5+3\left(-4\right)\right)\left(-3\right)-2}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

Multiply 3 and -4 to get -12.

$$\frac{\left(-5-12\right)\left(-3\right)-2}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

Subtract 12 from -5 to get -17.

$$\frac{-17\left(-3\right)-2}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

Multiply -17 and -3 to get 51.

$$\frac{51-2}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

Subtract 2 from 51 to get 49.

$$\frac{49}{\left(\frac{25-6\left(-5\right)}{-11}+21-32\right)\left(-3\right)-2}$$

Multiply 6 and -5 to get -30.

$$\frac{49}{\left(\frac{25-\left(-30\right)}{-11}+21-32\right)\left(-3\right)-2}$$

The opposite of -30 is 30.

$$\frac{49}{\left(\frac{25+30}{-11}+21-32\right)\left(-3\right)-2}$$

Add 25 and 30 to get 55.

$$\frac{49}{\left(\frac{55}{-11}+21-32\right)\left(-3\right)-2}$$

Divide 55 by -11 to get -5.

$$\frac{49}{\left(-5+21-32\right)\left(-3\right)-2}$$

Add -5 and 21 to get 16.

$$\frac{49}{\left(16-32\right)\left(-3\right)-2}$$

Subtract 32 from 16 to get -16.

$$\frac{49}{-16\left(-3\right)-2}$$

Multiply -16 and -3 to get 48.

$$\frac{49}{48-2}$$

Subtract 2 from 48 to get 46.

$$\frac{49}{46}$$

Factor

$$\frac{7 ^ {2}}{2 \cdot 23} = 1\frac{3}{46} = 1.065217391304348$$