Solve |(-2/3)-1-(-3)|/(-frac{2{3})^2+(1)^3}:-2/3+1/-frac{2{3}*(1)^2}

$$\frac { | ( - \frac { 2 } { 3 } ) - 1 - ( - 3 ) | } { ( - \frac { 2 } { 3 } ) ^ { 2 } + ( 1 ) ^ { 3 } } : \frac { - \frac { 2 } { 3 } + 1 } { - \frac { 2 } { 3 } \cdot ( 1 ) ^ { 2 } }$$

Evaluate

$$-\frac{24}{13}\approx -1.846153846$$

Solution Steps

Divide \frac{|-\frac{2}{3}-1-\left(-3\right)|}{\left(-\frac{2}{3}\right)^{2}+1^{3}} by \frac{-\frac{2}{3}+1}{-\frac{2}{3}\times 1^{2}} by multiplying \frac{|-\frac{2}{3}-1-\left(-3\right)|}{\left(-\frac{2}{3}\right)^{2}+1^{3}} by the reciprocal of \frac{-\frac{2}{3}+1}{-\frac{2}{3}\times 1^{2}}.

$$\frac{|-\frac{2}{3}-1-\left(-3\right)|\left(-\frac{2}{3}\right)\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{|-\frac{2}{3}-\frac{3}{3}-\left(-3\right)|\left(-\frac{2}{3}\right)\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

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

$$\frac{|\frac{-2-3}{3}-\left(-3\right)|\left(-\frac{2}{3}\right)\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

Subtract 3 from -2 to get -5.

$$\frac{|-\frac{5}{3}-\left(-3\right)|\left(-\frac{2}{3}\right)\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

The opposite of -3 is 3.

$$\frac{|-\frac{5}{3}+3|\left(-\frac{2}{3}\right)\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{|-\frac{5}{3}+\frac{9}{3}|\left(-\frac{2}{3}\right)\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

Since -\frac{5}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

$$\frac{|\frac{-5+9}{3}|\left(-\frac{2}{3}\right)\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

Add -5 and 9 to get 4.

$$\frac{|\frac{4}{3}|\left(-\frac{2}{3}\right)\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{4}{3} is \frac{4}{3}.

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

Multiply \frac{4}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{4\left(-2\right)}{3\times 3}.

$$\frac{\frac{-8}{9}\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$\frac{-\frac{8}{9}\times 1^{2}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{-\frac{8}{9}}{\left(\left(-\frac{2}{3}\right)^{2}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{-\frac{8}{9}}{\left(\frac{4}{9}+1^{3}\right)\left(-\frac{2}{3}+1\right)}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{-\frac{8}{9}}{\left(\frac{4}{9}+1\right)\left(-\frac{2}{3}+1\right)}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{-\frac{8}{9}}{\left(\frac{4}{9}+\frac{9}{9}\right)\left(-\frac{2}{3}+1\right)}$$

Since \frac{4}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{8}{9}}{\frac{4+9}{9}\left(-\frac{2}{3}+1\right)}$$

Add 4 and 9 to get 13.

$$\frac{-\frac{8}{9}}{\frac{13}{9}\left(-\frac{2}{3}+1\right)}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{-\frac{8}{9}}{\frac{13}{9}\left(-\frac{2}{3}+\frac{3}{3}\right)}$$

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

$$\frac{-\frac{8}{9}}{\frac{13}{9}\times \frac{-2+3}{3}}$$

Add -2 and 3 to get 1.

$$\frac{-\frac{8}{9}}{\frac{13}{9}\times \frac{1}{3}}$$

Multiply \frac{13}{9} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{8}{9}}{\frac{13\times 1}{9\times 3}}$$

Do the multiplications in the fraction \frac{13\times 1}{9\times 3}.

$$\frac{-\frac{8}{9}}{\frac{13}{27}}$$

Divide -\frac{8}{9} by \frac{13}{27} by multiplying -\frac{8}{9} by the reciprocal of \frac{13}{27}.

$$-\frac{8}{9}\times \frac{27}{13}$$

Multiply -\frac{8}{9} times \frac{27}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8\times 27}{9\times 13}$$

Do the multiplications in the fraction \frac{-8\times 27}{9\times 13}.

$$\frac{-216}{117}$$

Reduce the fraction \frac{-216}{117} to lowest terms by extracting and canceling out 9.

$$-\frac{24}{13}$$

Factor

$$-\frac{24}{13} = -1\frac{11}{13} = -1.8461538461538463$$