Solve each of the following equations for x.
Problem#1
(x)/(6) - (x)/(8)
MY answer: x = 24
Problem #2
(x)/(x-2) - (x+1)/(x) = (8)/(x^2-2x)
My answer is: 6 = x or x = 6
right on the first one.
check your math on the second one. i've done it twice and both times got (-10).
To solve these equations for x, let's go through each step and find the solutions:
Problem #1:
To solve the equation `(x/6) - (x/8)`, we need to combine the fractions by finding a common denominator.
The least common multiple (LCM) of 6 and 8 is 24. Multiplying each fraction by the necessary factor, we get:
`(x/6) * (4/4) - (x/8) * (3/3)`
Simplifying further, we have:
`(4x/24) - (3x/24)`
Combining like terms, we have:
`x/24`
Since there are no further steps to be taken, this equation is already simplified.
Therefore, the solution is: `x = 24`.
Problem #2:
To solve the equation `(x/(x-2)) - ((x+1)/x) = (8/(x^2-2x))`, let's first simplify the equation by finding a common denominator.
The common denominator for `(x/(x-2))` and `((x+1)/x)` is `x(x-2)`. Multiplying each term by the necessary factors, we get:
`x * (x/x) * (x/x-2) - (x-2) * ((x+1)/(x-2)) = (8/(x^2-2x)) * (x(x-2))`
Simplifying further, we have:
`x^2 - (x-2) * (x+1) = 8x`
Expanding the brackets and collecting like terms, we have:
`x^2 - (x^2 - x - 2) = 8x`
Simplifying further, we have:
`-x - 2 = 8x`
Combine the x terms to one side:
`-9x - 2 = 0`
Subtracting 2 from both sides, we get:
`-9x = 2`
Dividing both sides by -9 to isolate x, we have:
`x = -2/9`
Therefore, the solution to Problem #2 is `x = -2/9`.
It seems like your initial answer of x = 6 might not be correct, so please recheck your calculations for Problem #2.