Question

The following equation has denominators that contain variables. For this equation write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. Keeping the restrictions in mind, solve the equation.

2/x=4/5x+2
x=

Answer 1

X = 3/5

Explanation:

2/x=4/5x+2

Find the LCM of the denominator 5x and 1

2/x =4/5x + 2/1

2/x = (4 + 10x)/5x

Cross multiply the equation

2× 5x = (4+ 10x) × x

10x = 4x + 10x^2

Collect like term of the mixed number

10x - 4x = 10x^2

6x = 10x^2

Divide both side by 2x

6x/2x = {10x^2 } / 2x

3 = 5x

Divide both side by the coefficient of x

3/5 = 5x/5

X = 3/5