Question

(4-x):(x-4)+3=x -x+(-18:(x-4))=7 ((1-x):(x-1))+x=1

Answer 1

~~~~~TIGROVSKIY~~~~~

Answer 2

To solve the equations, let's go step by step:

1. (4-x)/(x-4) + 3 = x - x + (-18/(x-4)) = 7

Step 1: Simplify the expressions on each side of the equal sign.

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

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

Step 2: Simplify the expression on the left side of the equal sign.

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

Now, we have two equations. Let's solve them one by one.

Equation 1: (4-x)/(x-4) + 3 = 7

Step 1: Get rid of the denominator by multiplying both sides by (x-4).

(x-4) * [(4-x)/(x-4) + 3] = (x-4) * 7

Step 2: Simplify both sides.

(4-x) + 3(x-4) = 7(x-4)

Step 3: Expand and simplify further.

4 - x + 3x - 12 = 7x - 28

Step 4: Combine like terms.

2x - 8 = 7x - 28

Step 5: Bring all x terms to one side and the constant terms to the other side.

2x - 7x = -28 + 8

Step 6: Simplify.

-5x = -20

Step 7: Divide by -5 to isolate x.

x = 4

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

Step 1: Multiply both sides by (x-1) to eliminate the denominator.

(x-1) * [(1-x)/(x-1) + x] = (x-1) * 1

Step 2: Simplify both sides.

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

Step 3: Expand and simplify further.

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

Step 4: Combine like terms.

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

Step 5: Bring all terms to one side.

x^2 - 2x - x + 1 + 1 = 0

Step 6: Simplify.

x^2 - 3x + 2 = 0

Step 7: Factor the quadratic equation.

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

Step 8: Set each factor to zero and solve for x.

x - 1 = 0 -> x = 1 x - 2 = 0 -> x = 2

So, the solutions to the second equation are x = 1 and x = 2.

To summarize, the solutions to the given equations are: x = 4, x = 1, and x = 2.