Solve b^2+b-2/b+6-(c+4)=1/b+6

$$\frac { b ^ { 2 } + b - 2 } { b + 6 } - ( c + 4 ) = \frac { 1 } { b + 6 }$$

Solve for c

$$c=\frac{b^{2}-3b-27}{b+6}$$

$$b\neq -6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by b+6.

$$b^{2}+b-2-\left(c+4\right)\left(b+6\right)=1$$

Use the distributive property to multiply -1 by c+4.

$$b^{2}+b-2+\left(-c-4\right)\left(b+6\right)=1$$

Use the distributive property to multiply -c-4 by b+6.

$$b^{2}+b-2-cb-6c-4b-24=1$$

Combine b and -4b to get -3b.

$$b^{2}-3b-2-cb-6c-24=1$$

Subtract 24 from -2 to get -26.

$$b^{2}-3b-26-cb-6c=1$$

Subtract b^{2} from both sides.

$$-3b-26-cb-6c=1-b^{2}$$

Add 3b to both sides.

$$-26-cb-6c=1-b^{2}+3b$$

Add 26 to both sides.

$$-cb-6c=1-b^{2}+3b+26$$

Add 1 and 26 to get 27.

$$-cb-6c=27-b^{2}+3b$$

Combine all terms containing c.

$$\left(-b-6\right)c=27-b^{2}+3b$$

The equation is in standard form.

$$\left(-b-6\right)c=27+3b-b^{2}$$

Divide both sides by -b-6.

$$\frac{\left(-b-6\right)c}{-b-6}=\frac{27+3b-b^{2}}{-b-6}$$

Dividing by -b-6 undoes the multiplication by -b-6.

$$c=\frac{27+3b-b^{2}}{-b-6}$$

Divide 27-b^{2}+3b by -b-6.

$$c=-\frac{27+3b-b^{2}}{b+6}$$

Solve for b (complex solution)

$$b=\frac{\sqrt{c^{2}+30c+117}+c+3}{2}$$

$$b=\frac{-\sqrt{c^{2}+30c+117}+c+3}{2}$$

Solve for b

$$b=\frac{\sqrt{c^{2}+30c+117}+c+3}{2}$$

$$b=\frac{-\sqrt{c^{2}+30c+117}+c+3}{2}\text{, }c\geq 6\sqrt{3}-15\text{ or }c\leq -6\sqrt{3}-15$$