Solve 3/a-7+5/a^2-13a+42=7/a-6

$$\frac { 3 } { a - 7 } + \frac { 5 } { a ^ { 2 } - 13 a + 42 } = \frac { 7 } { a - 6 }$$

Solve for a

$$a=9$$

Steps for Solving Linear Equation

Variable a cannot be equal to any of the values 6,7 since division by zero is not defined. Multiply both sides of the equation by \left(a-7\right)\left(a-6\right), the least common multiple of a-7,a^{2}-13a+42,a-6.

$$\left(a-6\right)\times 3+5=\left(a-7\right)\times 7$$

Use the distributive property to multiply a-6 by 3.

$$3a-18+5=\left(a-7\right)\times 7$$

Add -18 and 5 to get -13.

$$3a-13=\left(a-7\right)\times 7$$

Use the distributive property to multiply a-7 by 7.

$$3a-13=7a-49$$

Subtract 7a from both sides.

$$3a-13-7a=-49$$

Combine 3a and -7a to get -4a.

$$-4a-13=-49$$

Add 13 to both sides.

$$-4a=-49+13$$

Add -49 and 13 to get -36.

$$-4a=-36$$

Divide both sides by -4.

$$a=\frac{-36}{-4}$$

Divide -36 by -4 to get 9.

$$a=9$$