Solve -3-2+6lnx+5-10lnx+4lnx/x^2

$$\frac { - 3 - 2 + 6 \ln x + 5 - 10 \ln x + 4 \ln x } { x ^ { 2 } }$$

Evaluate

$$0$$

Solution Steps

Subtract 2 from -3 to get -5.

$$\frac{-5+6\log_{e}\left(x\right)+5-10\log_{e}\left(x\right)+4\log_{e}\left(x\right)}{x^{2}}$$

Add -5 and 5 to get 0.

$$\frac{6\log_{e}\left(x\right)-10\log_{e}\left(x\right)+4\log_{e}\left(x\right)}{x^{2}}$$

Combine 6\log_{e}\left(x\right) and -10\log_{e}\left(x\right) to get -4\log_{e}\left(x\right).

$$\frac{-4\log_{e}\left(x\right)+4\log_{e}\left(x\right)}{x^{2}}$$

Combine -4\log_{e}\left(x\right) and 4\log_{e}\left(x\right) to get 0.

$$\frac{0}{x^{2}}$$

Zero divided by any non-zero term gives zero.

$$0$$

Factor

$$0$$