Solve 1/6!+1/7!=x/8!

$$\frac { 1 } { 6 ! } + \frac { 1 } { 7 ! } = \frac { x } { 8 ! }$$

Solve for x

$$x=64$$

Steps for Solving Linear Equation

The factorial of 6 is 720.

$$\frac{1}{720}+\frac{1}{7!}=\frac{x}{8!}$$

The factorial of 7 is 5040.

$$\frac{1}{720}+\frac{1}{5040}=\frac{x}{8!}$$

Least common multiple of 720 and 5040 is 5040. Convert \frac{1}{720} and \frac{1}{5040} to fractions with denominator 5040.

$$\frac{7}{5040}+\frac{1}{5040}=\frac{x}{8!}$$

Since \frac{7}{5040} and \frac{1}{5040} have the same denominator, add them by adding their numerators.

$$\frac{7+1}{5040}=\frac{x}{8!}$$

Add 7 and 1 to get 8.

$$\frac{8}{5040}=\frac{x}{8!}$$

Reduce the fraction \frac{8}{5040} to lowest terms by extracting and canceling out 8.

$$\frac{1}{630}=\frac{x}{8!}$$

The factorial of 8 is 40320.

$$\frac{1}{630}=\frac{x}{40320}$$

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

$$\frac{x}{40320}=\frac{1}{630}$$

Multiply both sides by 40320.

$$x=\frac{1}{630}\times 40320$$

Multiply \frac{1}{630} and 40320 to get \frac{40320}{630}.

$$x=\frac{40320}{630}$$

Divide 40320 by 630 to get 64.

$$x=64$$