Solve (x ^ 2 + 3x)/2 * ifx = 1/3 | 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

$$\frac{x^{2}+3x}{2}if\ x=\frac{1}{3}$$

Solve for f

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

Steps for Solving Linear Equation

Multiply both sides of the equation by $6$, the least common multiple of $2,3$.

$$3\left(x^{2}+3x\right)ifx=2$$

Multiply $3$ and $i$ to get $3i$.

$$3i\left(x^{2}+3x\right)fx=2$$

Use the distributive property to multiply $3i$ by $x^{2}+3x$.

$$\left(3ix^{2}+9ix\right)fx=2$$

Use the distributive property to multiply $3ix^{2}+9ix$ by $f$.

$$\left(3ix^{2}f+9ixf\right)x=2$$

Use the distributive property to multiply $3ix^{2}f+9ixf$ by $x$.

$$3ifx^{3}+9ifx^{2}=2$$

Combine all terms containing $f$.

$$\left(3ix^{3}+9ix^{2}\right)f=2$$

Divide both sides by $3ix^{3}+9ix^{2}$.

$$\frac{\left(3ix^{3}+9ix^{2}\right)f}{3ix^{3}+9ix^{2}}=\frac{2}{3ix^{3}+9ix^{2}}$$

Dividing by $3ix^{3}+9ix^{2}$ undoes the multiplication by $3ix^{3}+9ix^{2}$.

$$f=\frac{2}{3ix^{3}+9ix^{2}}$$

Divide $2$ by $3ix^{3}+9ix^{2}$.

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