Solve 3/c-3-1/c=28/9c-27

$$\frac { 3 } { c - 3 } - \frac { 1 } { c } = \frac { 28 } { 9 c - 27 }$$

Solve for c

$$c = \frac{27}{10} = 2\frac{7}{10} = 2.7$$

Steps for Solving Linear Equation

Variable c cannot be equal to any of the values 0,3 since division by zero is not defined. Multiply both sides of the equation by 9c\left(c-3\right), the least common multiple of c-3,c,9c-27.

$$9c\times 3-\left(9c-27\right)=c\times 28$$

Multiply 9 and 3 to get 27.

$$27c-\left(9c-27\right)=c\times 28$$

To find the opposite of 9c-27, find the opposite of each term.

$$27c-9c+27=c\times 28$$

Combine 27c and -9c to get 18c.

$$18c+27=c\times 28$$

Subtract c\times 28 from both sides.

$$18c+27-c\times 28=0$$

Combine 18c and -c\times 28 to get -10c.

$$-10c+27=0$$

Subtract 27 from both sides. Anything subtracted from zero gives its negation.

$$-10c=-27$$

Divide both sides by -10.

$$c=\frac{-27}{-10}$$

Fraction \frac{-27}{-10} can be simplified to \frac{27}{10} by removing the negative sign from both the numerator and the denominator.

$$c=\frac{27}{10}$$