Solve 2+(5-8-5)div-2/-3divfrac{1{3}+2(5)}=[1/4-2]^-1

$$\frac { 2 + ( 5 - 8 - 5 ) \div - 2 } { - 3 \div \frac { 1 } { 3 } + 2 ( 5 ) } = [ \frac { 1 } { 4 } - 2 ] ^ { - 1 }$$

Verify

Solution Steps

Subtract 8 from 5 to get -3.

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

Subtract 5 from -3 to get -8.

$$\frac{2+\frac{-8}{-2}}{\frac{-3}{\frac{1}{3}}+2\times 5}=\left(\frac{1}{4}-2\right)^{-1}$$

Divide -8 by -2 to get 4.

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

Add 2 and 4 to get 6.

$$\frac{6}{\frac{-3}{\frac{1}{3}}+2\times 5}=\left(\frac{1}{4}-2\right)^{-1}$$

Divide -3 by \frac{1}{3} by multiplying -3 by the reciprocal of \frac{1}{3}.

$$\frac{6}{-3\times 3+2\times 5}=\left(\frac{1}{4}-2\right)^{-1}$$

Multiply -3 and 3 to get -9.

$$\frac{6}{-9+2\times 5}=\left(\frac{1}{4}-2\right)^{-1}$$

Multiply 2 and 5 to get 10.

$$\frac{6}{-9+10}=\left(\frac{1}{4}-2\right)^{-1}$$

Add -9 and 10 to get 1.

$$\frac{6}{1}=\left(\frac{1}{4}-2\right)^{-1}$$

Anything divided by one gives itself.

$$6=\left(\frac{1}{4}-2\right)^{-1}$$

Subtract 2 from \frac{1}{4} to get -\frac{7}{4}.

$$6=\left(-\frac{7}{4}\right)^{-1}$$

Calculate -\frac{7}{4} to the power of -1 and get -\frac{4}{7}.

$$6=-\frac{4}{7}$$

Convert 6 to fraction \frac{42}{7}.

$$\frac{42}{7}=-\frac{4}{7}$$

Compare \frac{42}{7} and -\frac{4}{7}.

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