Solve 12/7=a+1/b+frac{1{c}}

$$1 \frac { 2 } { 7 } = a + \frac { 1 } { b + \frac { 1 } { c } }$$

Solve for a

$$a=\frac{9bc-7c+9}{7\left(bc+1\right)}$$

$$b\neq -\frac{1}{c}\text{ and }c\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 7.

$$1\times 7+2=7a+7\left(bc+1\right)^{-1}c$$

Multiply 1 and 7 to get 7.

$$7+2=7a+7\left(bc+1\right)^{-1}c$$

Add 7 and 2 to get 9.

$$9=7a+7\left(bc+1\right)^{-1}c$$

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

$$7a+7\left(bc+1\right)^{-1}c=9$$

Subtract 7\left(bc+1\right)^{-1}c from both sides.

$$7a=9-7\left(bc+1\right)^{-1}c$$

Reorder the terms.

$$7a=9-7\times \frac{1}{bc+1}c$$

Multiply both sides of the equation by bc+1.

$$7a\left(bc+1\right)=\left(bc+1\right)\times 9-7\times \frac{1}{bc+1}c\left(bc+1\right)$$

Use the distributive property to multiply 7a by bc+1.

$$7abc+7a=\left(bc+1\right)\times 9-7\times \frac{1}{bc+1}c\left(bc+1\right)$$

Use the distributive property to multiply bc+1 by 9.

$$7abc+7a=9bc+9-7\times \frac{1}{bc+1}c\left(bc+1\right)$$

Express -7\times \frac{1}{bc+1} as a single fraction.

$$7abc+7a=9bc+9+\frac{-7}{bc+1}c\left(bc+1\right)$$

Express \frac{-7}{bc+1}c as a single fraction.

$$7abc+7a=9bc+9+\frac{-7c}{bc+1}\left(bc+1\right)$$

Express \frac{-7c}{bc+1}\left(bc+1\right) as a single fraction.

$$7abc+7a=9bc+9+\frac{-7c\left(bc+1\right)}{bc+1}$$

Cancel out bc+1 in both numerator and denominator.

$$7abc+7a=9bc+9-7c$$

Combine all terms containing a.

$$\left(7bc+7\right)a=9bc+9-7c$$

The equation is in standard form.

$$\left(7bc+7\right)a=9bc-7c+9$$

Divide both sides by 7bc+7.

$$\frac{\left(7bc+7\right)a}{7bc+7}=\frac{9bc-7c+9}{7bc+7}$$

Dividing by 7bc+7 undoes the multiplication by 7bc+7.

$$a=\frac{9bc-7c+9}{7bc+7}$$

Divide 9bc-7c+9 by 7bc+7.

$$a=\frac{9bc-7c+9}{7\left(bc+1\right)}$$

Solve for b (complex solution)

$$b=-\frac{7a+7c-9}{c\left(7a-9\right)}$$

$$c\neq 0\text{ and }a\neq \frac{9}{7}$$

Solve for b

$$b=-\frac{7a+7c-9}{c\left(7a-9\right)}$$

$$a\neq \frac{9}{7}\text{ and }c\neq 0$$