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How do you simplify and find the restrictions for #(3b)/(b(b + 9))#?

Answer 1

See the solution process below:

To simplify this expression cancel the common term in the numerator and denominator:

#(3b)/(b(b + 9)) = (3color(red)(cancel(color(black)(b))))/(color(red)(cancel(color(black)(b)))(b + 9)) = 3/(b + 9)#

To find the restrictions we need to use the original form of the expression. Because we cannot divide by #0# we must solve for:

#b(b + 9) = 0#

To solve this we solve each term for 0:

#b = 0#

#b + 9 = 0#

#b + 9 - color(red)(9) = 0 - color(red)(9)#

#b + 0 = -9#

#b = -9#

The restrictions are:

#b != 0# and #b != -9#

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Answer 2

Kennedy Adams

To simplify the expression (3b)/(b(b + 9)), we can cancel out the common factor of b in the numerator and denominator. This simplifies the expression to 3/(b + 9).

To find the restrictions, we need to identify any values of b that would make the denominator equal to zero, as division by zero is undefined. In this case, the denominator b(b + 9) will be equal to zero when b = 0 or b = -9. Therefore, the restrictions for this expression are b ≠ 0 and b ≠ -9.

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Answer from HIX Tutor

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.