Algebra Ex 3.4-10th Std Maths-Book Back Question And Answer
Question 1.
Reduce each of the following rational expression to its lowest form.
(i) x2−1x2+x
Answer:
x2−1x2+x = (x+1)(x−1)x(x+1) = x−1x
(ii) x2−11x+18x2−4x+4
x2 – 11x + 18 = (x – 9) (x – 2)
x2 – 4x + 4 = (x – 2) (x – 2)
9x2 + 81x = 9x(x + 9)
x3 + 8x2 – 9x = x(x2 + 8x – 9)
= x (x + 9) (x – 1)
(iv) p2−3p−402p3−24p2+64p
p2 – 3p – 40 = (p – 8) (p + 5)
2p3 – 24p2 + 64p = 2p (p2 – 12p + 32)
= 2p (p – 8) (p – 4)
Question 2.
Find the excluded values , if any of the following expressions.
(i) yy2−25
Answer:
The expression yy2−25 is undefined
when y2 – 25 = 0
y2 – 52 = 0
(y + 5) (y – 5) = 0
y + 5 = 0 or y – 5 = 0
∵ y = -5 or y = 5
The excluded values are -5 and 5
(ii) tt2−5t+6
Answer:
The expression tt2−5t+6 is undefined
when t2 – 5t + 6 = 0
(t – 3) (t – 2) = 0
t – 3 = 0 or t – 2 = 0
t = 3 or t = 2
The excluded values are 2 and 3
(iii) x2+6x+8x2+x−2
Answer:
x2 + 6x + 8 = (x + 4) (x + 2)
x2 + x – 2 = (x + 2) (x – 1)
The expression x+4x−1 is undefined
when x – 1 = 0
∵ x = 1
The excluded value is 1
(iv) x3−27x3+x2−6x
x3 – 27 = x3 – 33
= (x – 3) (x2 + x + 3)
x3 + x2 – 6x = x(x2 + x – 6) = x (x + 3) (x – 2)
when x (x + 3) (x – 2) = 0
x = 0 or x + 3 = 0 or x – 2 = 0
x = 0 or x = -3 or x = 2
The excluded values are 0 , -3 and 2
