Solve y=frac{sqrt{23+1}}{x+1}

$$y = \frac { \sqrt { 23 + 1 } } { x + 1 }$$

Solve for x

$$x=-1+\frac{2\sqrt{6}}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by x+1.

$$y\left(x+1\right)=\sqrt{23+1}$$

Use the distributive property to multiply y by x+1.

$$yx+y=\sqrt{23+1}$$

Add 23 and 1 to get 24.

$$yx+y=\sqrt{24}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$yx+y=2\sqrt{6}$$

Subtract y from both sides.

$$yx=2\sqrt{6}-y$$

The equation is in standard form.

$$yx=-y+2\sqrt{6}$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{-y+2\sqrt{6}}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{-y+2\sqrt{6}}{y}$$

Divide 2\sqrt{6}-y by y.

$$x=-1+\frac{2\sqrt{6}}{y}$$

Variable x cannot be equal to -1.

$$x=-1+\frac{2\sqrt{6}}{y}\text{, }x\neq -1$$

Solve for y

$$y=\frac{2\sqrt{6}}{x+1}$$

$$x\neq -1$$