Divide.
[(X^2 +6+9)/(X-1)]/(X^2-9)/(x^2-2x+1)
• [(x+3)(x-1)]/(x-3)
• [(x-3)(x+1)]/(x+3)
• [(x+3)(x+1)/(x-3)
• [(x-3)(x-1)]/x+3)
How?
assuming you meant 6x in the first term.
that first term factors to (x+3)(x+3)
now in the nenominator, (x-3)(x+3)/((x-1)^2
I see in the numerator
(x+3)^2/(x-1)*(x-1)^2/(x-3)(x+3)
then
(x+3)(x-1)/(x-3)
check that.
That helps
To simplify the given expression, we need to divide the numerator by the denominator. The given expression can be written as:
\[((x^2 + 6 + 9) / (x - 1)) / ((x^2 - 9) / (x^2 - 2x + 1))\]
First, let's simplify the numerator and denominator separately:
Numerator:
\(x^2 + 6 + 9\) can be simplified to \(x^2 + 15\)
Denominator:
\(x^2 - 9\) can be factored using difference of squares: \((x - 3)(x + 3)\)
\(x^2 - 2x + 1\) can be factored using perfect square trinomial: \((x - 1)^2\)
Now, let's substitute the simplified numerator and denominator into the expression:
\(((x^2 + 15) / (x - 1)) / (((x - 3)(x + 3)) / ((x - 1)^2))\)
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of \(((x - 3)(x + 3)) / ((x - 1)^2)\) is \(((x - 1)^2) / ((x - 3)(x + 3))\). So, we can rewrite the expression as:
\(((x^2 + 15) / (x - 1)) * (((x - 1)^2) / ((x - 3)(x + 3)))\)
Next, we can simplify the expression by canceling out common factors:
\(((x^2 + 15) * (x - 1)^2) / ((x - 1) * (x - 3)(x + 3))\)
We can further simplify the expression by expanding \((x - 1)^2\) and cancelling out common factors:
\((x^2 + 15) * (x^2 - 2x + 1) / ((x - 1) * (x - 3)(x + 3))\)
\((x^4 + x^2 - 2x^3 - 2x + 15x^2 + 15) / ((x - 1) * (x - 3)(x + 3))\)
Finally, we can simplify the expression even further:
\((x^4 - 2x^3 + 16x^2 + 13x + 15) / ((x - 1) * (x - 3)(x + 3))\)
Thus, the simplified expression is \((x^4 - 2x^3 + 16x^2 + 13x + 15) / ((x - 1) * (x - 3)(x + 3))\).
Out of the options provided, none of them match the simplified expression obtained.