Solve a ^ v + 1/(av) = 3 | 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

$$a^{v}+\frac{1}{av}=3$$

Solve for a

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

Steps for Solving Linear Equation

Variable $a$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $ax$.

$$axx^{2}+1=3ax$$

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$ax^{3}+1=3ax$$

Subtract $3ax$ from both sides.

$$ax^{3}+1-3ax=0$$

Subtract $1$ from both sides. Anything subtracted from zero gives its negation.

$$ax^{3}-3ax=-1$$

Combine all terms containing $a$.

$$\left(x^{3}-3x\right)a=-1$$

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

$$\frac{\left(x^{3}-3x\right)a}{x^{3}-3x}=-\frac{1}{x^{3}-3x}$$

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

$$a=-\frac{1}{x^{3}-3x}$$

Divide $-1$ by $x^{3}-3x$.

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

Variable $a$ cannot be equal to $0$.

$$a=-\frac{1}{x\left(x^{2}-3\right)}\text{, }a\neq 0$$