Solve m/p-11=m/12+3/2

$$\frac{ m }{ p } -11 = \frac{ m }{ 12 } + \frac{ 3 }{ 2 }$$

Solve for m

$$m=\frac{150p}{12-p}$$

$$p\neq 12\text{ and }p\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12p, the least common multiple of p,12,2.

$$12m+12p\left(-11\right)=pm+12p\times \frac{3}{2}$$

Multiply 12 and -11 to get -132.

$$12m-132p=pm+12p\times \frac{3}{2}$$

Multiply 12 and \frac{3}{2} to get 18.

$$12m-132p=pm+18p$$

Subtract pm from both sides.

$$12m-132p-pm=18p$$

Add 132p to both sides.

$$12m-pm=18p+132p$$

Combine 18p and 132p to get 150p.

$$12m-pm=150p$$

Combine all terms containing m.

$$\left(12-p\right)m=150p$$

Divide both sides by -p+12.

$$\frac{\left(12-p\right)m}{12-p}=\frac{150p}{12-p}$$

Dividing by -p+12 undoes the multiplication by -p+12.

$$m=\frac{150p}{12-p}$$

Solve for p

$$p=\frac{12m}{m+150}$$

$$m\neq 0\text{ and }m\neq -150$$

Steps for Solving Linear Equation

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12p, the least common multiple of p,12,2.

$$12m+12p\left(-11\right)=pm+12p\times \frac{3}{2}$$

Multiply 12 and -11 to get -132.

$$12m-132p=pm+12p\times \frac{3}{2}$$

Multiply 12 and \frac{3}{2} to get 18.

$$12m-132p=pm+18p$$

Subtract pm from both sides.

$$12m-132p-pm=18p$$

Subtract 18p from both sides.

$$12m-132p-pm-18p=0$$

Combine -132p and -18p to get -150p.

$$12m-150p-pm=0$$

Subtract 12m from both sides. Anything subtracted from zero gives its negation.

$$-150p-pm=-12m$$

Combine all terms containing p.

$$\left(-150-m\right)p=-12m$$

The equation is in standard form.

$$\left(-m-150\right)p=-12m$$

Divide both sides by -m-150.

$$\frac{\left(-m-150\right)p}{-m-150}=-\frac{12m}{-m-150}$$

Dividing by -m-150 undoes the multiplication by -m-150.

$$p=-\frac{12m}{-m-150}$$

Divide -12m by -m-150.

$$p=\frac{12m}{m+150}$$

Variable p cannot be equal to 0.

$$p=\frac{12m}{m+150}\text{, }p\neq 0$$