Solve a/c+dx=e/p+gx

$$\frac { a } { c + d x } = \frac { e } { p + g x }$$

Solve for a

$$a=\frac{e\left(dx+c\right)}{gx+p}$$

$$c\neq -dx\text{ and }p\neq -gx$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(dx+c\right)\left(gx+p\right), the least common multiple of c+dx,p+gx.

$$\left(gx+p\right)a=\left(dx+c\right)e$$

Use the distributive property to multiply gx+p by a.

$$gxa+pa=\left(dx+c\right)e$$

Use the distributive property to multiply dx+c by e.

$$gxa+pa=dxe+ce$$

Combine all terms containing a.

$$\left(gx+p\right)a=dxe+ce$$

The equation is in standard form.

$$\left(gx+p\right)a=edx+ec$$

Divide both sides by p+gx.

$$\frac{\left(gx+p\right)a}{gx+p}=\frac{e\left(dx+c\right)}{gx+p}$$

Dividing by p+gx undoes the multiplication by p+gx.

$$a=\frac{e\left(dx+c\right)}{gx+p}$$

Solve for c

$$c=\frac{agx-edx+ap}{e}$$

$$p\neq -gx\text{ and }a\neq 0$$