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put this solution on YOUR website! x^2-1/x^2+x*3x/1-x please help simplify
x² - 1 3x
-------- · -------
x² + x 1 - x
All the numerators and denominators
are in descending order except 1 - x
So arrange the 1 - x in descending order,
as -x + 1
x² - 1 3x
-------- · -------
x² + x -x + 1
Factor the upper left numerator as the
difference of two squares:
(x - 1)(x + 1) 3x
---------------- · --------
x² + x -x + 1
Factor the lower left denominator by
factoring out x
(x - 1)(x + 1) 3x
---------------- · --------
x(x + 1) -x + 1
Factor the lower right denominator by
factoring out -1, which causes a
sign change inside the parentheses:
(x - 1)(x + 1) 3x
---------------- · ----------
x(x + 1) -1(x - 1)
Indicate the multiplication of the
numerators and denominators so that
we have just one fraction. Write the
shorter factors first:
3x(x - 1)(x + 1)
-------------------
-1x(x + 1)(x - 1)
Cancel the x's
1
3x(x - 1)(x + 1)
-------------------
-1x(x + 1)(x - 1)
1
Cancel the (x - 1)'s
1 1
3x(x - 1)(x + 1)
-------------------
-1x(x + 1)(x - 1)
1 1
Cancel the (x + 1)'s
1 1 1
3x(x - 1)(x + 1)
-------------------
-1x(x + 1)(x - 1)
1 1 1
All that's left is
3
----
-1
which is just
-3
Edwin
