Solve 40=30+frac{30-5+{f}_{1}}{{f}_{2}}30

$$40 = 30+ \frac{ 30-5+ { f }_{ 1 } }{ { f }_{ 2 } } 30$$

Solve for f_1

$$f_{1}=\frac{f_{2}-75}{3}$$

$$f_{2}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by f_{2}.

$$40f_{2}=f_{2}\times 30+\left(30-5+f_{1}\right)\times 30$$

Subtract 5 from 30 to get 25.

$$40f_{2}=f_{2}\times 30+\left(25+f_{1}\right)\times 30$$

Use the distributive property to multiply 25+f_{1} by 30.

$$40f_{2}=f_{2}\times 30+750+30f_{1}$$

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

$$f_{2}\times 30+750+30f_{1}=40f_{2}$$

Subtract f_{2}\times 30 from both sides.

$$750+30f_{1}=40f_{2}-f_{2}\times 30$$

Combine 40f_{2} and -f_{2}\times 30 to get 10f_{2}.

$$750+30f_{1}=10f_{2}$$

Subtract 750 from both sides.

$$30f_{1}=10f_{2}-750$$

Divide both sides by 30.

$$\frac{30f_{1}}{30}=\frac{10f_{2}-750}{30}$$

Dividing by 30 undoes the multiplication by 30.

$$f_{1}=\frac{10f_{2}-750}{30}$$

Divide -750+10f_{2} by 30.

$$f_{1}=\frac{f_{2}}{3}-25$$

Solve for f_2

$$f_{2}=3\left(f_{1}+25\right)$$

$$f_{1}\neq -25$$

Steps for Solving Linear Equation

Variable f_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by f_{2}.

$$40f_{2}=f_{2}\times 30+\left(30-5+f_{1}\right)\times 30$$

Subtract 5 from 30 to get 25.

$$40f_{2}=f_{2}\times 30+\left(25+f_{1}\right)\times 30$$

Use the distributive property to multiply 25+f_{1} by 30.

$$40f_{2}=f_{2}\times 30+750+30f_{1}$$

Subtract f_{2}\times 30 from both sides.

$$40f_{2}-f_{2}\times 30=750+30f_{1}$$

Combine 40f_{2} and -f_{2}\times 30 to get 10f_{2}.

$$10f_{2}=750+30f_{1}$$

The equation is in standard form.

$$10f_{2}=30f_{1}+750$$

Divide both sides by 10.

$$\frac{10f_{2}}{10}=\frac{30f_{1}+750}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$f_{2}=\frac{30f_{1}+750}{10}$$

Divide 750+30f_{1} by 10.

$$f_{2}=3f_{1}+75$$

Variable f_{2} cannot be equal to 0.

$$f_{2}=3f_{1}+75\text{, }f_{2}\neq 0$$