Open Ended Write a rational equation that can be solved by f

Open Ended Write a rational equation that can be solved by first multiplying each side by 5(a+ 2) Explain why the equation x + 1/x - 1 = 1 + 1/x - 1. has no solution. State what expression by which you multiply each side of x/x - 3 + 1/3 = 1 in order to solve the equation. 2 - 3/a = 2/3 6a - 9 = 2a 4a = 9 a = 2.25 2 - 3/a = 2/3 2 - 9 = 2a -7 = 2a -3.5 = a What value(s) of x cannot be a solution? Find the Error Jeff and Dustin are solving. 2-3/a = 2/3 Who is correct? Explain your reasoning, explain how find the LCD of a rational equation. Tell why it is necessary to check your solutions when solving a rational equation. Give an example in your explanation.

Solution

1) 4a/(5(a+2) = 2/5

So multiply both sides by 5(a+2) to solve :

4a= 2(5(a+2)/5

4a = 2(a+2) ; 4a = 2a + 4

2a = 4 ; a= 2 ( solution)

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

Multiply both sides by (x-1)

x(x-1) + 1 = 1(x-1) +x

x^2 - x+ 1 = x -1 + x

x^2 -3x + 2 =0

x^2 - 2x -x +2 =0 ;

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

x = 1 ; x= 2

Now x=1 is not a solution because if we plug x=1 in the original equation denominato becomes 0