How to solve (r+m)/(2r-m)=h

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (r+m)/(2r-m)=h | Equatix

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Question

$$\frac{ r+m }{ 2r-m } =h$$

Solve for h

$h=-\frac{m+r}{m-2r}$
$r\neq \frac{m}{2}$

Steps for Solving Linear Equation

Multiply both sides of the equation by $-m+2r$.

$$r+m=h\left(-m+2r\right)$$

Use the distributive property to multiply $h$ by $-m+2r$.

$$r+m=-hm+2hr$$

Swap sides so that all variable terms are on the left hand side.

$$-hm+2hr=r+m$$

Combine all terms containing $h$.

$$\left(-m+2r\right)h=r+m$$

The equation is in standard form.

$$\left(2r-m\right)h=m+r$$

Divide both sides by $2r-m$.

$$\frac{\left(2r-m\right)h}{2r-m}=\frac{m+r}{2r-m}$$

Dividing by $2r-m$ undoes the multiplication by $2r-m$.

$$h=\frac{m+r}{2r-m}$$

Show Solution

Solve for m

$\left\{\begin{matrix}m=-\frac{r\left(1-2h\right)}{h+1}\text{, }&r\neq 0\text{ and }h\neq -1\\m\neq 0\text{, }&r=0\text{ and }h=-1\end{matrix}\right.$