2.) x+1/ x-2= x+3 divide by x-1 --- (4.)1/x - 5/6x = 2/3 -------(6.) x-7/x+1 - x-4 /3x-2 =0

Question

please help me with these examples of solveing each equation and checking the soultion!

Answer 1

(x+1)/(x-2) = (x+3)/(x-1)

cross multiply

(x+1)*(x-1) = (x+3)*(x-2)

expands to

x^2 -x +x -1 = x^2 -2x +3x -6

the x^2 on each side cancel, and consolidate the xs

-1 = x -6

add 6 to both sides

x=5. Put that back into the original equation and see if it is correct.



1/x - 5/6x =2/3

Multiply both sides by x

1/1 - 5/6 =2x/3

so 2x/3 - 1-5/6 = 1/6

Multiply both sides by 3 and divide by 2

x= 3/12 =1/4 Put that back into the original equation and see if it is correct.


(x-7)/(x+1) - (x-4)/(3x-2) = 0

Add (x-4)/(3x-2) to both sides now gives

(x-7)/(x+1) = (x-4)/(3x-2)

cross multiply

(x-7)*(3x-2) = (x-4)*(x+1)

and expand
3x^2 -21x -2x +14 = x^2 -4x +1x -4

subtract (x^2 -4x +1x -4) from both sides and simplify the xs

2x^2 -20x +18 = 0

the solutions to ax^2 +bx +c = 0 are:
{-b +/- sqrt(b^2-4*a*c)}/2a

so {20 +/- sqrt (20^2 - 4*2*18)}/2*2

do the math and you end up with

1 and 9 Put these numbers back into the original equation and see if they are correct.