Rational equations

Question

Solve the rational equations
1. 1/x = 6/5x + 1

2. X/x-1 - 2/x = 1/x-1

3. X/3 - 4/3x =1

Answer 1

1. 1/x = 6/5x + 1

multiply every term by 5x(LCD) you will get 

5= 6 + 5x

-1=5x

-1/5=x

 

2.x/x-1 -2/x =1/x-1

multiply every term by x(x-1)(LCD) you will get

 

x^2 -2(x-1)=x

simplifying wil give you

x^2 -2x +2 =x

Subtracting x from both  sides

X^2 -3x+2 = 0

(x-2)(x-1)=0

x={2, 1}

 

3. x/3-4/3x = 1

Multiply each term by LCD (3x) will give you 

x^2 -4= 3x

x^2 -3x-4=0

(x-4)(x+1)=0

x={4,-1}