To solve this equation, we first need to find a common denominator for the two fractions on the left side of the equation. In this case, the least common denominator is 21^2 - x^2, which is equal to (21 + x)(21 - x).
So, we rewrite the equation with the common denominator:
(21 + x)/(21 + x) + (21 - x)/(21 - x) = 42
Now we can combine the fractions:
(21 + x + 21 - x)/(21^2 - x^2) = 42
Simplifying the numerator, we get:
42/(441 - x^2) = 42
Now we can multiply both sides by (441 - x^2) to get rid of the fraction:
42 = 42(441 - x^2)
Now we can distribute the 42 on the right side:
42 = 18492 - 42x^2
Rearranging the equation to isolate the variable, we get:
42x^2 = 18492 - 42
Dividing by 42 on both sides, we get:
x^2 = (18492 - 42)/42
x^2 = 440
Taking the square root of both sides, we get:
x = ±√440
x = ±20.976
Therefore, the solution to the equation is x = ±20.976.
To solve this equation, we first need to find a common denominator for the two fractions on the left side of the equation. In this case, the least common denominator is 21^2 - x^2, which is equal to (21 + x)(21 - x).
So, we rewrite the equation with the common denominator:
(21 + x)/(21 + x) + (21 - x)/(21 - x) = 42
Now we can combine the fractions:
(21 + x + 21 - x)/(21^2 - x^2) = 42
Simplifying the numerator, we get:
42/(441 - x^2) = 42
Now we can multiply both sides by (441 - x^2) to get rid of the fraction:
42 = 42(441 - x^2)
Now we can distribute the 42 on the right side:
42 = 18492 - 42x^2
Rearranging the equation to isolate the variable, we get:
42x^2 = 18492 - 42
Dividing by 42 on both sides, we get:
x^2 = (18492 - 42)/42
x^2 = 440
Taking the square root of both sides, we get:
x = ±√440
x = ±20.976
Therefore, the solution to the equation is x = ±20.976.