Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify the rational expression. State any restrictions on the variable. (t^(2)+t-6)/(t^(2)-9)

Simplify the rational expression. State any restrictions on the variable.\newlinet2+t−6t2−9 \frac{t^{2}+t-6}{t^{2}-9}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Determine end behavior of polynomial and rational functionsright chevron icon

Full solution

Q. Simplify the rational expression. State any restrictions on the variable.\newlinet2+t−6t2−9 \frac{t^{2}+t-6}{t^{2}-9}
  1. Factor Numerator and Denominator: Factor the numerator and the denominator.\newlineNumerator: t2+t−6 t^2 + t - 6 factors to (t+3)(t−2) (t + 3)(t - 2) .\newlineDenominator: t2−9 t^2 - 9 factors to (t+3)(t−3) (t + 3)(t - 3) .
  2. Simplify by Canceling Common Factors: Simplify the expression by canceling common factors.\newline(t+3)(t−2)(t+3)(t−3)\frac{(t + 3)(t - 2)}{(t + 3)(t - 3)} simplifies to t−2t−3\frac{t - 2}{t - 3}, assuming t+3≠0 t + 3 \neq 0 .
  3. State Variable Restrictions: State the restrictions on the variable.\newlineSince division by zero is undefined, t≠−3 t \neq -3 and t≠3 t \neq 3 .

More problems from Determine end behavior of polynomial and rational functions

Question
Let f(x)=6x33x+2 f(x)=\frac{6 x^{3}}{3 x+2} .\newlineFind lim⁡x→∞f(x) \lim _{x \rightarrow \infty} f(x) .\newlineChoose 11 answer:\newline(A) 22\newline(B) 33\newline(C) 00\newline(D) The limit is unbounded
Get tutor helpright-arrow

Posted 9 months ago

Question
What is the average value of x3−9x x^{3}-9 x on the interval −1≤x≤3 -1 \leq x \leq 3 ?
Get tutor helpright-arrow

Posted 7 months ago

Question
Determine the following limit in simplest form. If the limit is infinite, state that the limit does not exist (DNE).\newlinelim⁡x→∞−3x+x47+8x2+10x \lim _{x \rightarrow \infty} \frac{\sqrt{-3 x+x^{4}}}{7+8 x^{2}+10 x} \newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline1−1+5y−4 1-1+5 y-4
Get tutor helpright-arrow

Posted 9 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline4y−2+3−4x−x 4 y-2+3-4 x-x
Get tutor helpright-arrow

Posted 9 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline−5x+5x−5+4x -5 x+5 x-5+4 x \newlineYou must answer all questions above in order to submit.
Get tutor helpright-arrow

Posted 9 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline5y−7y−2+6−6 5 y-7 y-2+6-6
Get tutor helpright-arrow

Posted 9 months ago

Question
Click and drag like terms onto each other to simplify fully.\newline−5x−6+2x−1−3y−1 -5 x-6+2 x-1-3 y-1
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the slope-intercept form for the line satisfying the conditions.\newlineslope −6-6, passing through \newline(0,1)(0,1)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the equation. Check your solution\newline−5(5n−5)=30-5(5n-5)=30\newline
Get tutor helpright-arrow

Posted 6 months ago

View all (27)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant