University:
Highline College
Course:
MATHP 141 | Precalculus I Plus Extra Support
Academic year:

2022
Views:

170

Pages:

2
Author:

Jared Bowers

Workshop #13 1. Find all values of the variable for which the rational expression is undeﬁned (a) 1 x 1 x−1 x−1 (c) x−1 (b) 2x (x − 1)(x − 2) 2x + 1 (e) 5x − 1 3 − 2x (f) 3x2 + 4x + 1 (d) 2. Pick numbers a and b to show the following cancellation is not valid 2a + b =2+b a 3. Pick an x to show the following cancellation is not valid + 5 −2) (x 3 =3+5 (x −2) 4. Simplify the following rational expressions, assume no denominators are zero (a) (2x + 1) − (2x − 2) 3 · (2x + 1) (b) (x + 2) 4x + 8 x2 + 4x + 3 x2 − 4x − 21 a 2 + b2 (d) a+b (c) 5. Perform the operation and simplify, assume no denominators are zero 2 2 x + 3x + 2 3x2 + 5x − 2 x − x − 12 2 ÷ (a) (x + 6x + 8) · (c) x2 − 16 12x2 − 13x + 3 4x2 + 5x − 6 3 x + 2x2 − x − 2 2x2 + 5x − 3 x2 − 2x − 15 2x2 − 5x + 2 x2 + 2x − 35 (b) (d) 2 · ÷ · x2 + 5x + 6 x2 − 6x + 5 x + 2x − 3 x2 − 9x + 14 x2 − 6x + 5 6. Find the least common multiple of the following pairs (a) 12 and 16 (b) 9x3 and 3x4 (c) x − 3 and x2 − 9 (d) x4 y 2 z 5 and wxy 3 z 4 (e) 2x3 + 6x2 and x2 + 3x 7. Pick numbers a and b to show the following equality is not valid a a2 = 2. b b 8. Add or subtract the fractions and simplify (a) 2 6 + 5 25 (b) 2 3 + 15 9 a c + b d 3 2x − (g) x + 1 3x − 2 3 2 x+3 (h) − + x + 1 x − 1 x2 − 1 1 1 − 9 6 1 1 (d) − 9 6a 3 1 (e) + 2 2a 4a (f) (c) 9. Simplify 2 + 4x x 2x + + x2 − 25 x2 + 2x − 35 (x − 5)(x2 + 12x + 35) 10. Simplify the following, assume no denominators are zero (a) (b) (c) (d) (e) (x + 2)2 − 8x (x − 2) 2 1 1 − x+2 x−2 2 x + 2x − 3 4x 2 · 2+ 2 − x −1 x−1 2x2 + 4x x 4 ÷ x+2+ x2 − 6x + 8 x−2 2 x x+1 2x + x − +x ÷ x − 1 2x − 2 2x