The way you typed it, ....
1/5x+15 - 3/x+3=5
it becomes a quadratic with 2 irrational solutions.
since your choices are single rational numbers, you must have meant:
1/(5x+15) - 3/(x+3)=5
1/(5(x+3) - 3/(x+3) = 5
-14/(5/(x+3)) = 5
25(x+3) = -14
25x + 75 = -14
25x = -89
x = -89/25 , which is choice A
Solve the equation.
1/5x+15 - 3/x+3=5
A. x= -89/25
B. x= 89/25
C. x= -61/25
D. x= 61/25*****
2 answers
Your answer is correct but not complete.
Multiply both sides by sides by 5 x
x² + 75 x - 15 + 15 x = 25
x² + 90 x - 15 = 25 x
Subtract 25 x to both sides
x² + 65 x - 15 = 0
The solutions are:
( 65 - √4285 ) / 2 ≈ ( 65 - 65.46 ) / 2 ≈ - 0.23
and
( 65 + √4285 ) / 2 ≈ ( 65 + 65.46 ) / 2 ≈ 65.23
Multiply both sides by sides by 5 x
x² + 75 x - 15 + 15 x = 25
x² + 90 x - 15 = 25 x
Subtract 25 x to both sides
x² + 65 x - 15 = 0
The solutions are:
( 65 - √4285 ) / 2 ≈ ( 65 - 65.46 ) / 2 ≈ - 0.23
and
( 65 + √4285 ) / 2 ≈ ( 65 + 65.46 ) / 2 ≈ 65.23