4 over x =9 over 5 - 7x-4 divided by 5x
4/x = 9/5 - 7x-4/5x
Step 1: Subtract the two fractions on the right side of the equation. To do this, however, you need to find the lowest common denominator. You have 5 and 5x. The lowest common denominator for these is 5x. So, the first fraction needs to be multiplied by x, both numerator and denominator, to get a 5x on the bottom.
The second fraction remains the same, because the denominator did not have to be changed. The fraction remains at 7x-4/5x.
You may now subtract, since you have common denominators.
9x-(7x-4) = 2x+4. Place this over 5x and make it equal to 4/x.
So, you now have 4/x = 2x+4/5x.
Step 2: Cross-multiply. (5x)(4) = 20x; (x)(2x+4) = 2x^2+4x.
So, you now have 2x^2 + 4x = 20x.
Step 3: Subtract 20x from both sides.
Result: 2x^2-16x = 0.
Step 4: Factor out a 2x.
Result: 2x(x-8) = 0.
Step 5: Set each 'x' factor equal to 0.
2x = 0
x-8 = 0
For 2x = 0, x must be 0 (2 x 0 = 0).
For x-8 = 0, x must be 8 (8-8 = 0).
Answer: x = 8. x cannot be 0 because the first fraction, 4/x, would then be undefined. A fraction can never have 0 as the denominator.
I hope this helps.