Use the questions below to keep track or key concepts from this lessons study activity. 1) Fill in the blanks. A rational expression is a comparison of two polynomials, expressed as a 2) Main Idea: You can find the value of a rational expression if you know the value of the variable. Rule Example To evaluate a rational expression, Evaluate X when x = 2. a specific number for x +1 every variable in the expression and simplify. +73) Main Idea: A rational expression equals zero when its numerator equals zero. Rule Example To find the value or values that makes a Find the values of x that make this rational expression equal to zero, find expression equal to zero: any value that makes the equal to zero. X - 1 (x+ 1) (x - 5) x- 1=0 X = The expression equals zero when X = 4) Main Idea: A rational expression is undefined when its denominator equals zero.4) Main Idea: A rational expression is undefined when its denominator equals zero. Rule Example To find the value or values that makes a Find the values of x that make this rational expression undefined, find any expression undefined: value that makes the equal to zero. X - 1 (x+ 1)(x - 5) x +1=0 X - 5=0 X = X = The expression is undefined at X= and x =5) Main Idea: You sometimes have to factor the numerator or denominator to find values that make a rational function undefined or equal to zero. Factoring Tips Example Find the values of x that make this . Look for a common factor to factor rational expression undefined: out. 5 . Look for a difference of squares. x3 - x A2 - B2 = (A + B)(A - B) . Use coefficients and constants. ax +bxx+c=(xx1p)(atq) ros= a p. q = c