Simplify Expressions, etc.

Sep 2015
2
0
Tucson
1) Rewrite the given expression in the form of t^B where B is simplified as much as possible: [t^3-n t^7n]/[(t^2)^n]
[HR][/HR]2) Simplify completely as a fraction in factored form: 15c-3c^2/c^2-c-20
[HR][/HR]3)What values of x make the expression sqr(x+3)/x-2 undefined? Express your final answer using interval notation.
 
Feb 2014
1,748
651
United States
In the future, please do not ask multiple questions in a single thread. And please either show your work so we can see WHERE you need help or say what prevents you from even starting.

Question 1: is what you mean to simplify $\dfrac{t^{(3 - n)} * t^{(7n)}}{(t^2)^n}.$

That is not what you wrote.

How do the laws of exponents help you?

Question 2: is what you mean to simplify $\dfrac{15c - 3c^2}{c^2 - c - 20}.$

That is not what you wrote.

If you factor the numerator, what do you get? If you factor the denominator, what do you get? How might you proceed next.

Question 3: are there any values of x such that $\sqrt{x + 3}$ is not a real number?

Are there any values of x such that $x - 2$ is not allowed as a divisor?
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
1) Rewrite the given expression in the form of t^B where B is simplified as much as possible: [t^(3-n) t^(7n)]/[(t^2)^n]
[HR][/HR]2) Simplify completely as a fraction in factored form: (15c-3c^2)/(c^2-c-20)
[HR][/HR]3)What values of x make the expression sqr(x+3)/(x-2) undefined? Express your final answer using interval notation.
In future, use parentheses as grouping symbols to make expressions clear to the reader.


1) $\dfrac{t^{3-n} \cdot t^{7n}}{(t^2)^n} = t^{3-n} \cdot \dfrac{t^{7n}}{t^{2n}} = t^{3-n} \cdot t^{5n} = \, ?$ ... finish it


2) try factoring both the numerator and denominator and see if they have any common factors that will divide out

3) for the numerator, $x+3 \ge 0$ why? for the denominator, $x-2 \ne 0$ why?