Solve 3*(-3/4)^-2+6*(3^-1/4)-4/7*(frac{-3{4})^-1+2}+4=

$$\frac { 3 \cdot ( \frac { - 3 } { 4 } ) ^ { - 2 } + 6 \cdot ( \frac { 3 ^ { - 1 } } { 4 } ) - 4 } { 7 \cdot ( \frac { - 3 } { 4 } ) ^ { - 1 } + 2 } + 4 =$$

Evaluate

$$\frac{15}{4}=3.75$$

Solution Steps

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{3\left(-\frac{3}{4}\right)^{-2}+6\times \frac{3^{-1}}{4}-4}{7\times \left(\frac{-3}{4}\right)^{-1}+2}+4$$

Calculate -\frac{3}{4} to the power of -2 and get \frac{16}{9}.

$$\frac{3\times \frac{16}{9}+6\times \frac{3^{-1}}{4}-4}{7\times \left(\frac{-3}{4}\right)^{-1}+2}+4$$

Multiply 3 and \frac{16}{9} to get \frac{16}{3}.

$$\frac{\frac{16}{3}+6\times \frac{3^{-1}}{4}-4}{7\times \left(\frac{-3}{4}\right)^{-1}+2}+4$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{\frac{16}{3}+6\times \frac{\frac{1}{3}}{4}-4}{7\times \left(\frac{-3}{4}\right)^{-1}+2}+4$$

Express \frac{\frac{1}{3}}{4} as a single fraction.

$$\frac{\frac{16}{3}+6\times \frac{1}{3\times 4}-4}{7\times \left(\frac{-3}{4}\right)^{-1}+2}+4$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{16}{3}+6\times \frac{1}{12}-4}{7\times \left(\frac{-3}{4}\right)^{-1}+2}+4$$

Multiply 6 and \frac{1}{12} to get \frac{1}{2}.

$$\frac{\frac{16}{3}+\frac{1}{2}-4}{7\times \left(\frac{-3}{4}\right)^{-1}+2}+4$$

Add \frac{16}{3} and \frac{1}{2} to get \frac{35}{6}.

$$\frac{\frac{35}{6}-4}{7\times \left(\frac{-3}{4}\right)^{-1}+2}+4$$

Subtract 4 from \frac{35}{6} to get \frac{11}{6}.

$$\frac{\frac{11}{6}}{7\times \left(\frac{-3}{4}\right)^{-1}+2}+4$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{\frac{11}{6}}{7\left(-\frac{3}{4}\right)^{-1}+2}+4$$

Calculate -\frac{3}{4} to the power of -1 and get -\frac{4}{3}.

$$\frac{\frac{11}{6}}{7\left(-\frac{4}{3}\right)+2}+4$$

Multiply 7 and -\frac{4}{3} to get -\frac{28}{3}.

$$\frac{\frac{11}{6}}{-\frac{28}{3}+2}+4$$

Add -\frac{28}{3} and 2 to get -\frac{22}{3}.

$$\frac{\frac{11}{6}}{-\frac{22}{3}}+4$$

Divide \frac{11}{6} by -\frac{22}{3} by multiplying \frac{11}{6} by the reciprocal of -\frac{22}{3}.

$$\frac{11}{6}\left(-\frac{3}{22}\right)+4$$

Multiply \frac{11}{6} and -\frac{3}{22} to get -\frac{1}{4}.

$$-\frac{1}{4}+4$$

Add -\frac{1}{4} and 4 to get \frac{15}{4}.

$$\frac{15}{4}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {2}} = 3\frac{3}{4} = 3.75$$