Question

-1 -5x+4
----- = ----
x+2 x-5

Answer 1

A. x=1,5
B. x=1
C. x=5
D. no solution

Answer 2

Solve for x over the real numbers:
-1/(x+2) = (4-5 x)/(x-5)
Write the left hand side as a single fraction.
Bring -1/(x+2) together using the common denominator -x-2:
1/(-2-x) = (4-5 x)/(x-5)
Multiply both sides by a polynomial to clear fractions.
Cross multiply:
x-5 = (4-5 x) (-2-x)
Write the quadratic polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
x-5 = 5 x^2+6 x-8
Move everything to the left hand side.
Subtract 5 x^2+6 x-8 from both sides:
-5 x^2-5 x+3 = 0
Write the quadratic equation in standard form.
Divide both sides by -5:
x^2+x-3/5 = 0
Solve the quadratic equation by completing the square.
Add 3/5 to both sides:
x^2+x = 3/5
Take one half of the coefficient of x and square it, then add it to both sides.
Add 1/4 to both sides:
x^2+x+1/4 = 17/20
Factor the left hand side.
Write the left hand side as a square:
(x+1/2)^2 = 17/20
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x+1/2 = sqrt(17/5)/2 or x+1/2 = -sqrt(17/5)/2
Look at the first equation: Solve for x.
Subtract 1/2 from both sides:
x = sqrt(17/5)/2-1/2 or x+1/2 = -sqrt(17/5)/2
Look at the second equation: Solve for x.
Subtract 1/2 from both sides:
Answer: x = sqrt(17/5)/2-1/2 or x = -1/2-sqrt(17/5)/2

Answer 3

so no solution?

Answer 4

@nincompoop