Question

Rational expressions
P and Q no of sumplify of Rational expression​

Answer 1

Answer:

p)

(3x - 8) / (x - 2)(x - 3)

Step-by-step explanation:

p)

First term : (x - 1) / (x² - 3x + 2)

Denominator: x² - 3x + 2

=> x² - 2x - x + 2

=> x(x - 2) - 1(x - 2)

=> (x - 1)(x - 2)

=> (x - 1) / (x² - 3x + 2) = (x - 1) / (x - 1)(x - 2) = 1 / (x - 2)

Second term : (x - 2) / (x² - 5x + 6)

Denominator: x² - 5x + 6

=> x² - 2x - 3x + 6

=> x(x - 2) - 3(x - 2)

=> (x - 3)(x - 2)

=> (x - 3) / (x² - 5x + 6) = (x - 3) / (x - 3)(x - 2) = 1 / (x - 2)

Third term : (x - 5) / (x² - 8x + 15)

Denominator: x² - 8x + 15

=> x² - 3x - 5x + 15

=> x(x - 3) - 5(x - 3)

=> (x - 5)(x - 3)

=> (x - 5) / (x² - 8x + 15) = (x - 5) / (x - 5)(x - 3) = 1 / (x - 3)

Adding all the terms, we get

(1 / (x - 2)) + (1 / (x - 2)) + (1 / (x - 3))

=> (2 / (x - 2)) + (1 / (x - 3))

Cross multiplying, we get

=> (2(x - 3) + (x - 2)) / (x - 2)(x - 3)

=> (2x - 6 + x - 2) / (x - 2)(x - 3)

=> (3x - 8) / (x - 2)(x - 3)

You can solve q in a similar way