Solve If f(x) = (sqrt(x + 2))/(3 - 3x ^ 2) for which values of x is | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$f ( x ) = \frac { \sqrt { x + 2 } } { 3 - 3 x ^ { 2 } } , x$$

Solve for f (complex solution)

$f=\frac{\sqrt{x+2}}{3\left(x-x^{3}\right)}$
$x\neq 1\text{ and }x\neq -1\text{ and }x\neq 0$

Steps for Solving Linear Equation

Multiply both sides of the equation by $3\left(x-1\right)\left(-x-1\right)$.

$$fx\times 3\left(x-1\right)\left(-x-1\right)=\sqrt{x+2}$$

Use the distributive property to multiply $fx\times 3$ by $x-1$.

$$\left(3fx^{2}-fx\times 3\right)\left(-x-1\right)=\sqrt{x+2}$$

Multiply $-1$ and $3$ to get $-3$.

$$\left(3fx^{2}-3fx\right)\left(-x-1\right)=\sqrt{x+2}$$

Use the distributive property to multiply $3fx^{2}-3fx$ by $-x-1$ and combine like terms.

$$-3fx^{3}+3fx=\sqrt{x+2}$$

Combine all terms containing $f$.

$$\left(-3x^{3}+3x\right)f=\sqrt{x+2}$$

The equation is in standard form.

$$\left(3x-3x^{3}\right)f=\sqrt{x+2}$$

Divide both sides by $3x-3x^{3}$.

$$\frac{\left(3x-3x^{3}\right)f}{3x-3x^{3}}=\frac{\sqrt{x+2}}{3x-3x^{3}}$$

Dividing by $3x-3x^{3}$ undoes the multiplication by $3x-3x^{3}$.

$$f=\frac{\sqrt{x+2}}{3x-3x^{3}}$$

Divide $\sqrt{x+2}$ by $3x-3x^{3}$.

$$f=\frac{\sqrt{x+2}}{3x\left(1-x^{2}\right)}$$

Solve for f

$f=\frac{\sqrt{x+2}}{3\left(x-x^{3}\right)}$
$x\neq 0\text{ and }x\geq -2\text{ and }|x|\neq 1$

Steps for Solving Linear Equation

Multiply both sides of the equation by $3\left(x-1\right)\left(-x-1\right)$.

$$fx\times 3\left(x-1\right)\left(-x-1\right)=\sqrt{x+2}$$

Use the distributive property to multiply $fx\times 3$ by $x-1$.

$$\left(3fx^{2}-fx\times 3\right)\left(-x-1\right)=\sqrt{x+2}$$

Multiply $-1$ and $3$ to get $-3$.

$$\left(3fx^{2}-3fx\right)\left(-x-1\right)=\sqrt{x+2}$$

Use the distributive property to multiply $3fx^{2}-3fx$ by $-x-1$ and combine like terms.

$$-3fx^{3}+3fx=\sqrt{x+2}$$

Combine all terms containing $f$.

$$\left(-3x^{3}+3x\right)f=\sqrt{x+2}$$

The equation is in standard form.

$$\left(3x-3x^{3}\right)f=\sqrt{x+2}$$

Divide both sides by $3x-3x^{3}$.

$$\frac{\left(3x-3x^{3}\right)f}{3x-3x^{3}}=\frac{\sqrt{x+2}}{3x-3x^{3}}$$

Dividing by $3x-3x^{3}$ undoes the multiplication by $3x-3x^{3}$.

$$f=\frac{\sqrt{x+2}}{3x-3x^{3}}$$

Divide $\sqrt{x+2}$ by $3x-3x^{3}$.

$$f=\frac{\sqrt{x+2}}{3x\left(1-x^{2}\right)}$$