Solve a/3+3/5=5a/7+7/9

$$\frac { a } { 3 } + \frac { 3 } { 5 } = \frac { 5 a } { 7 } + \frac { 7 } { 9 }$$

Solve for a

$$a=-\frac{7}{15}\approx -0.466666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 315, the least common multiple of 3,5,7,9.

$$105a+189=45\times 5a+245$$

Multiply 45 and 5 to get 225.

$$105a+189=225a+245$$

Subtract 225a from both sides.

$$105a+189-225a=245$$

Combine 105a and -225a to get -120a.

$$-120a+189=245$$

Subtract 189 from both sides.

$$-120a=245-189$$

Subtract 189 from 245 to get 56.

$$-120a=56$$

Divide both sides by -120.

$$a=\frac{56}{-120}$$

Reduce the fraction \frac{56}{-120} to lowest terms by extracting and canceling out 8.

$$a=-\frac{7}{15}$$