Simplify. State the nonpermissible values.
(3t^2+3t-6/2t^2-2t-4)(4t^2+4t-24/3t^2+6t-9)
This is the way I tried solving this:
3t(t-1)6(t-1)/2t(t-1)4(t-1)*4t(t-2)12(t-2)/3t(t+1)9(t-1)
(3)(t)(t-1)(2)(3)(t-1)/(2)(t)(t-1)(2)(2)(t-1)*(2)(2)(t)(t-2)(2)(2)(3)(t-2)/(3)(t)(t-1)(3)(3)(t-1)
After cancelling out all the terms I am left with:
(2)(t-2)(t-2)/(t-1)(t-1)
^ I cant cancel anything off now. But the answer is supposed to be :
2(t+2)/t+1
^ How do I get that answer?
(3t^2+3t-6)(4t^2+4t-24)
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(2t^2-2t-4)(3t^2+6t-9)
3(t^2+t-2)(4)(t^2+t-6)
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2(t-2)(t+1)(3)(t+3)(t-1)
3(t+2)(t-1)(4)(t+3)(t-2)
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2(t-2)(t+1)(3)(t+3)(t-1)
(2) (t+2) / (t+1)
2
Thank you so much Damon :)
You are welcome.
By the way that is undefined if t = -1 so I suppose that might be what is meant by "non-permissible"
Thank you and yeah nonpermissible is another word for restrictions.
To simplify the given expression and find the nonpermissible values, we need to factor the numerator and denominator, cancel out common factors, and identify any values that would make the denominator equal to zero (nonpermissible values).
Let's start by factoring the numerator and denominator separately:
Numerator:
3t^2 + 3t - 6
= 3(t^2 + t - 2)
= 3(t - 1)(t + 2)
Denominator:
2t^2 - 2t - 4
= 2(t^2 - t - 2)
= 2(t - 2)(t + 1)
Now, we can rewrite the expression as:
[(3(t - 1)(t + 2))/(2(t - 2)(t + 1))] * [(4t^2 + 4t - 24)/(3t^2 + 6t - 9)]
Next, we can cancel out common factors between the numerator and denominator:
[(3(t - 1)(t + 2))/(2(t - 2)(t + 1))] * [(4(t^2 + t - 6))/(3(t^2 + 2t - 3))]
Simplifying further:
[(3(t - 1)(t + 2))/(2(t - 2)(t + 1))] * [(4(t - 1)(t + 3))/(3(t - 1)(t + 3))]
Now, the common factors in the numerator and denominator can be canceled out:
[(3(t - 1)(t + 2))/(2(t - 2)(t + 1))] * [(4)/(3)]
This simplifies to:
(12(t - 1)(t + 2))/(6(t - 2)(t + 1))
Finally, we can cancel out the common factor between the numerator and denominator:
(2(t - 1)(t + 2))/(t - 2)(t + 1)
The simplified expression is:
2(t - 1)(t + 2)/(t - 2)(t + 1)
To find the nonpermissible values, we need to identify any values of 't' that would make the denominator equal to zero. In this case, the nonpermissible values are t = -1 and t = 2 since they would result in division by zero, which is undefined.
Therefore, the nonpermissible values for this expression are t = -1 and t = 2.