Rational Expressions
1-x^2/x
Second expression
2b-2/2b^2-8
please show steps
1 - x^2/x = 1-x
(1-x^2)/x = 1/x - x
(2b-2)/(2b^2-8) = (b-1)/(b^2-4) = (b-1) / (b-2)(b+2)
Not sure just what you're after
The expressions are to be factored
To simplify the first rational expression, 1 - x^2 / x, you first need to find a common denominator between 1 and x.
The common denominator is x. So, rewrite 1 as x / x.
Now, the expression becomes (x - x^2) / x.
Next, factor out x from the numerator (x - x^2) to get x(1 - x) / x.
Now, cancel out the x in the numerator and denominator to get (1 - x) / 1.
Therefore, the simplified expression is 1 - x.
Moving on to the second expression, 2b - 2 / 2b^2 - 8, first factor out a 2 from the numerator and denominator.
This gives you 2(b - 1) / 2(b^2 - 4).
Next, factor the denominator as the difference of squares:
2(b - 1) / 2(b + 2)(b - 2).
Now, cancel out the common factor of 2 from the numerator and denominator:
(b - 1) / (b + 2)(b - 2).
Therefore, the simplified expression is (b - 1) / (b + 2)(b - 2).