Solving rational equations?

Question

1. (1/m^2-m) + (1/m)=5/m^2-m

2. (1/r-2) + (1/r^2-7r+10)=6/r-2

3. 1/x= (6/5x) + 1

4. 1=(v+2/v-4) + (7v - 42/v-4)

5. r-4/5r=(1/5r) + (1)

6. (r+5/r^2-2r) - 1= 1/r^2-2r

7. (a-2/a-3) - 1= 3/a+2

Answer 1

(1)

2 + m = 5

m = 5 - 2

m = 3

Solution is m = 3

Answer 2

(2)

r² - 6r + 8 = 6 ( r² - 7r + 10 )

r² - 6r + 8 = 6r² - 42r + 60

6r² - 42r + 60 - r² + 6r - 8 = 0

5r² - 36r + 52 = 0

The solution is { 2 , 5.2 }

Answer 3

(3)

The solution is x = -1/5

Answer 4

(4)

v - 4 = v + 2 + 7v - 42

v - 4 = 8v - 40

8v - v = 40 - 4

Answer 5

(5)

5r² - 4 = 1 + 5r

5r² - 5r - 1 - 4 = 0

5r² - 5r - 5= 0

r² - r - 1= 0

Answer 6

(6)

The given rational equation is

r² - 3r - 4 = 0

r² - 4r + r - 4 = 0

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

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

r = -1 , 4

The solution is r = { -1 , 4 }

Answer 7

(7)

The given rational equation is