Answer:
a) x = 0 is the solution to the equation.
b) x = any real number except 2
Explanation:
Hi there!
a) First, let´s write the equation:
(x-8) / (x-4) = 2
Now let´s solve it for x. Let´s start subtracting 2 to both sides of the equation
[(x-8) / (x-4)] - 2 = 0
Let´s subtract both terms, the least common multiple is (x-4)
[x-8 - 2(x - 4)] / (x-4) = 0
Apply distributive property
(x - 8 - 2x + 8) / (x - 4) = 0
-x / (x-4) = 0
x = 0
Now, let´s check the solution:
(x-8) / (x-4) = 2
x = 0
0-8 / 0-4 = 2
-8/-4 = 2
2 = 2
Then x = 0 is the solution to the equation.
b) Let´s write the equation:
(4x-8)/(x-2)=4
Let´s proceed in the same way as in a)
Subtract 4 to both sides of the equation.
(4x-8)/(x-2) - 4 = 0
Subtract both terms
[4x - 8 - 4(x-2)] / (x-2) = 0
Apply distributive property
(4x -8 - 4x + 8) / (x -2) = 0
0/(x-2) = 0
x can be any real number except 2 because it would make the denominator zero.