Solve AB C = L^ -1 * LT^ 2 L^ 2 | 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

$$\frac{AB}{C}=\frac{L^{-1}\times LT^{2}}{L^{2}}$$

Solve for A

$\left\{\begin{matrix}A=\frac{\left(\frac{T}{L}\right)^{2}C}{B}\text{, }&L\neq 0\text{ and }B\neq 0\text{ and }C\neq 0\\A\in \mathrm{R}\text{, }&T=0\text{ and }B=0\text{ and }L\neq 0\text{ and }C\neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $CL^{2}$, the least common multiple of $C,L^{2}$.

$$L^{2}AB=CL^{-1}LT^{2}$$

Reorder the terms.

$$ABL^{2}=\frac{1}{L}CLT^{2}$$

Multiply both sides of the equation by $L$.

$$ABL^{2}L=1CLT^{2}$$

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

$$ABL^{3}=1CLT^{2}$$

Reorder the terms.

$$ABL^{3}=CLT^{2}$$

The equation is in standard form.

$$BL^{3}A=CLT^{2}$$

Divide both sides by $BL^{3}$.

$$\frac{BL^{3}A}{BL^{3}}=\frac{CLT^{2}}{BL^{3}}$$

Dividing by $BL^{3}$ undoes the multiplication by $BL^{3}$.

$$A=\frac{CLT^{2}}{BL^{3}}$$

Divide $CLT^{2}$ by $BL^{3}$.

$$A=\frac{CT^{2}}{BL^{2}}$$

Solve for B

$\left\{\begin{matrix}B=\frac{\left(\frac{T}{L}\right)^{2}C}{A}\text{, }&L\neq 0\text{ and }A\neq 0\text{ and }C\neq 0\\B\in \mathrm{R}\text{, }&T=0\text{ and }A=0\text{ and }L\neq 0\text{ and }C\neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $CL^{2}$, the least common multiple of $C,L^{2}$.

$$L^{2}AB=CL^{-1}LT^{2}$$

Reorder the terms.

$$ABL^{2}=\frac{1}{L}CLT^{2}$$

Multiply both sides of the equation by $L$.

$$ABL^{2}L=1CLT^{2}$$

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

$$ABL^{3}=1CLT^{2}$$

Reorder the terms.

$$ABL^{3}=CLT^{2}$$

The equation is in standard form.

$$AL^{3}B=CLT^{2}$$

Divide both sides by $AL^{3}$.

$$\frac{AL^{3}B}{AL^{3}}=\frac{CLT^{2}}{AL^{3}}$$

Dividing by $AL^{3}$ undoes the multiplication by $AL^{3}$.

$$B=\frac{CLT^{2}}{AL^{3}}$$

Divide $CLT^{2}$ by $AL^{3}$.

$$B=\frac{CT^{2}}{AL^{2}}$$