4. Simplify. start fraction x over 6 x minus x squared end fraction (1 point)
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x/(6x-x^2) = 1/(6-x)
Correct! To simplify the expression x/(6x-x^2), you can first factor out x from both the numerator and denominator, giving you:
x/(6x-x^2) = x/(x(6-x))
Then, you can cancel out the common factor of x, which leaves you with:
x/(6x-x^2) = 1/(6-x)
To simplify the expression, start by factoring out the common term, "x":
x/6x - x^2
Next, simplify the expression further to cancel out the common factors in the numerator and denominator:
x/(6x) - x^2/(6x)
Since both fractions have a common denominator of 6x, you can combine them by subtracting the numerators:
(x - x^2)/(6x)
Now, let's simplify the expression by factoring out the greatest common factor from the numerator. In this case, the greatest common factor is x:
x(1 - x)/(6x)
Notice that there is a common factor of x in both the numerator and denominator. You can cancel out the common factor of x to simplify the expression further:
(1 - x)/6
Therefore, the simplified expression is (1 - x)/6.