How do you simplify #(10k^2+55k+75)/(20k^2-10k-150)# and find any non permissible values?
Use Ruffini or solution of second grade equation to find roots.
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To simplify the expression (10k^2+55k+75)/(20k^2-10k-150) and find any non-permissible values, we can factorize the numerator and denominator and then cancel out any common factors.
The numerator can be factored as (5k+15)(2k+5), and the denominator can be factored as (2k-15)(10k+10).
After factoring, we can cancel out the common factors, which are (5k+15) and (2k-15).
Therefore, the simplified expression is (2k+5)/(10k+10).
To find the non-permissible values, we need to identify any values of k that would make the denominator equal to zero.
Setting the denominator (10k+10) equal to zero and solving for k, we get k = -1.
Hence, the non-permissible value is k = -1.
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To simplify the expression ( \frac{10k^2 + 55k + 75}{20k^2 - 10k - 150} ) and find any non-permissible values, you factor both the numerator and denominator, then cancel out common factors. The non-permissible values are any values of ( k ) that make the denominator equal to zero.
Factoring the numerator: [ 10k^2 + 55k + 75 = 5(2k^2 + 11k + 15) ] [ = 5(2k^2 + 10k + k + 15) ] [ = 5(2k(k + 5) + 1(k + 5)) ] [ = 5(k + 5)(2k + 1) ]
Factoring the denominator: [ 20k^2 - 10k - 150 = 10(2k^2 - k - 15) ] [ = 10(2k^2 - 6k + 5k - 15) ] [ = 10(2k(k - 3) + 5(k - 3)) ] [ = 10(k - 3)(2k + 5) ]
Now, simplify the expression: [ \frac{10k^2 + 55k + 75}{20k^2 - 10k - 150} = \frac{5(k + 5)(2k + 1)}{10(k - 3)(2k + 5)} ]
Canceling out common factors: [ \frac{10k^2 + 55k + 75}{20k^2 - 10k - 150} = \frac{5(k + 5)}{2(k - 3)} ]
The non-permissible values are ( k = 3 ) and ( k = -\frac{5}{2} ), which make the denominator equal to zero.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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