To solve this equation, we need to first find a common denominator for the fractions on the left side of the equation. The common denominator is (20-x)(20+x).
So, rewrite the equation with the common denominator:
(48(20+x) + 48(20-x)) / ((20-x)(20+x)) = 5
Now, simplify the numerator:
48(20+x) + 48(20-x) = 48(20+x+20-x = 48(40 = 1920
So, the equation becomes:
1920 / ((20-x)(20+x)) = 5
Now, multiply both sides of the equation by ((20-x)(20+x)) to eliminate the denominator:
1920 = 5((20-x)(20+x) 1920 = 5(400-x^2)
Now, distribute the 5:
1920 = 2000 - 5x^2
Rearrange the equation to form a quadratic equation:
5x^2 = 2000 - 192 5x^2 = 8 x^2 = 1 x = ±4
Therefore, the solutions to the equation are x = 4 and x = -4.
To solve this equation, we need to first find a common denominator for the fractions on the left side of the equation. The common denominator is (20-x)(20+x).
So, rewrite the equation with the common denominator:
(48(20+x) + 48(20-x)) / ((20-x)(20+x)) = 5
Now, simplify the numerator:
48(20+x) + 48(20-x) = 48(20+x+20-x
= 48(40
= 1920
So, the equation becomes:
1920 / ((20-x)(20+x)) = 5
Now, multiply both sides of the equation by ((20-x)(20+x)) to eliminate the denominator:
1920 = 5((20-x)(20+x)
1920 = 5(400-x^2)
Now, distribute the 5:
1920 = 2000 - 5x^2
Rearrange the equation to form a quadratic equation:
5x^2 = 2000 - 192
5x^2 = 8
x^2 = 1
x = ±4
Therefore, the solutions to the equation are x = 4 and x = -4.