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\frac{21}{x-8}=\frac{1}{21}
Divide both sides by 21.
21\times 21=x-8
Variable x cannot be equal to 8 since division by zero is not defined. Multiply both sides of the equation by 21\left(x-8\right), the least common multiple of x-8,21.
441=x-8
Multiply 21 and 21 to get 441.
x-8=441
Swap sides so that all variable terms are on the left hand side.
x=441+8
Add 8 to both sides.
x=449
Add 441 and 8 to get 449.