Problem 1) √4 - x = -2

x -2 x -2

Problem 2) √x + 2 - x = 0

Was confused on the answers; please re-advise

Problem 1) √4 - x = -2

x -2 x -2

Problem 2) √x + 2 - x = 0

Was confused on the answers; please re-advise

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sqrt(4) = 2.

For 2 - x/(x-2) = -2/(x-2) start by multiplying through by (x-2) to get the variable out of the denominator. This gives:

2*(x-2) - x = -2. Expand this out, then combine the constant terms on one side and variable terms on the other.

2*x - 2*2 - x = -2

2*x - x = 4 - 2 Factor out the coefficients in front of x

(2-1)*x = 2 Divide to isolate x

x = 2

If you set x = 2 in the original equation, the result is to divide by 0 so it is not a valid solution.

For sqrt(x) + 2 - x = 0, I like to do this with a substitution by defining another variable y = sqrt(x).

The new equation becomes

y + 2 - y^{2} = 0, multiply by -1

y^{2} -y - 2 = 0

(y-2)(y+1) = 0

y = 2, -1

Since y = sqrt(x), x = y^2, so:

x = 4, 1

However, plugging these back into the original equation shows that only x =4 is a valid solution. This is because the sqrt(x) cannot equal (-1).