Solve -3k/2+9k-5/6=11k+8/k

$$- \frac { 3 k } { 2 } + \frac { 9 k - 5 } { 6 } = \frac { 11 k + 8 } { k }$$

Solve for k

$$k=-\frac{48}{71}\approx -0.676056338$$

Steps for Solving Linear Equation

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6k, the least common multiple of 2,6,k.

$$-3k\times 3k+k\left(9k-5\right)=6\left(11k+8\right)$$

Multiply 3k and 3k to get \left(3k\right)^{2}.

$$-\left(3k\right)^{2}+k\left(9k-5\right)=6\left(11k+8\right)$$

Expand \left(3k\right)^{2}.

$$-3^{2}k^{2}+k\left(9k-5\right)=6\left(11k+8\right)$$

Calculate 3 to the power of 2 and get 9.

$$-9k^{2}+k\left(9k-5\right)=6\left(11k+8\right)$$

Use the distributive property to multiply k by 9k-5.

$$-9k^{2}+9k^{2}-5k=6\left(11k+8\right)$$

Use the distributive property to multiply 6 by 11k+8.

$$-9k^{2}+9k^{2}-5k=66k+48$$

Subtract 66k from both sides.

$$-9k^{2}+9k^{2}-5k-66k=48$$

Combine -5k and -66k to get -71k.

$$-9k^{2}+9k^{2}-71k=48$$

Combine -9k^{2} and 9k^{2} to get 0.

$$-71k=48$$

Divide both sides by -71.

$$k=\frac{48}{-71}$$

Fraction \frac{48}{-71} can be rewritten as -\frac{48}{71} by extracting the negative sign.

$$k=-\frac{48}{71}$$