Solve operatorname{h}(x)=x^2+6^x-27/x^2-8x+7

$$\operatorname { h } ( x ) = \frac { x ^ { 2 } + 6 ^ { x } - 27 } { x ^ { 2 } - 8 x + 7 }$$

Solve for h

$$h=-\frac{27-6^{x}-x^{2}}{x\left(x-7\right)\left(x-1\right)}$$

$$x\neq 1\text{ and }x\neq 7\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-7\right)\left(x-1\right).

$$hx\left(x-7\right)\left(x-1\right)=x^{2}+6^{x}-27$$

Use the distributive property to multiply hx by x-7.

$$\left(hx^{2}-7hx\right)\left(x-1\right)=x^{2}+6^{x}-27$$

Use the distributive property to multiply hx^{2}-7hx by x-1 and combine like terms.

$$hx^{3}-8hx^{2}+7hx=x^{2}+6^{x}-27$$

Combine all terms containing h.

$$\left(x^{3}-8x^{2}+7x\right)h=x^{2}+6^{x}-27$$

Divide both sides by -8x^{2}+x^{3}+7x.

$$\frac{\left(x^{3}-8x^{2}+7x\right)h}{x^{3}-8x^{2}+7x}=\frac{x^{2}+6^{x}-27}{x^{3}-8x^{2}+7x}$$

Dividing by -8x^{2}+x^{3}+7x undoes the multiplication by -8x^{2}+x^{3}+7x.

$$h=\frac{x^{2}+6^{x}-27}{x^{3}-8x^{2}+7x}$$

Divide x^{2}+6^{x}-27 by -8x^{2}+x^{3}+7x.

$$h=\frac{x^{2}+6^{x}-27}{x\left(x-7\right)\left(x-1\right)}$$