Question

What is the solution to the rational equation 1/5+3/x-5=9/20

Answer 1

Solve for x over the real numbers:
-5 + 1/5 + 3/x = 9/20

-5 + 1/5 + 3/x = 3/x - 24/5:
3/x - 24/5 = 9/20

Bring 3/x - 24/5 together using the common denominator 5 x:
-(3 (8 x - 5))/(5 x) = 9/20

Cross multiply:
-60 (8 x - 5) = 45 x

Expand out terms of the left hand side:
300 - 480 x = 45 x

Subtract 45 x + 300 from both sides:
-525 x = -300

Divide both sides by -525:
Answer: x = 4/7