Question

X-9/3=56/x+4 solve for x

Answer 1

To solve the equation x - 9/3 = 56/x + 4 for x, multiply both sides by x, distribute and simplify, factor out x, set each factor equal to zero, and solve for x to get the solutions 0 and 63.

Step-by-step explanation:

To solve the equation x - 9/3 = 56/x + 4 for x:

1. Multiply both sides by x to get rid of the fraction: x(x) - 9/3(x) = 56 + 4(x)
2. Distribute and simplify:
   `x^2 - 3x = 56x + 4x`
3. Combine like terms:
   `x^2 - 63x = 0`
4. Factor out x: x(x - 63) = 0
5. Set each factor equal to zero: x = 0 or x - 63 = 0
6. Solve for x: x = 0 or x = 63

Therefore, the solutions for x are 0 and 63.

Answer 2

x = sqrt(273)/2 - 1/2 or x = -1/2 - sqrt(273)/2

Step-by-step explanation:

Solve for x:

x - 3 = 56/(x + 4)

Cross multiply:

(x - 3) (x + 4) = 56

Expand out terms of the left hand side:

x^2 + x - 12 = 56

Add 12 to both sides:

x^2 + x = 68

Add 1/4 to both sides:

x^2 + x + 1/4 = 273/4

Write the left hand side as a square:

(x + 1/2)^2 = 273/4

Take the square root of both sides:

x + 1/2 = sqrt(273)/2 or x + 1/2 = -sqrt(273)/2

Subtract 1/2 from both sides:

x = sqrt(273)/2 - 1/2 or x + 1/2 = -sqrt(273)/2

Subtract 1/2 from both sides:

Answer: x = sqrt(273)/2 - 1/2 or x = -1/2 - sqrt(273)/2