Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4

Students can download Maths Chapter 3 Algebra Ex 3.4 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.4

Question 1.
Reduce each of the following rational expression to its lowest form.
(i) \(\frac{x^{2}-1}{x^{2}+x}\)
Answer:
\(\frac{x^{2}-1}{x^{2}+x}\) = \(\frac{(x+1)(x-1)}{x(x+1)}\) = \(\frac { x-1 }{ x } \)

(ii) \(\frac{x^{2}-11 x+18}{x^{2}-4 x+4}\)
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 1
x2 – 11x + 18 = (x – 9) (x – 2)
x2 – 4x + 4 = (x – 2) (x – 2)
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 2
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 3

Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4

(iii) \(\frac{9 x^{2}+81 x}{x^{3}+8 x^{2}-9 x}\)
9x2 + 81x = 9x(x + 9)
x3 + 8x2 – 9x = x(x2 + 8x – 9)
= x (x + 9) (x – 1)
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 4

(iv) \(\frac{p^{2}-3 p-40}{2 p^{3}-24 p^{2}+64 p}\)
p2 – 3p – 40 = (p – 8) (p + 5)
2p3 – 24p2 + 64p = 2p (p2 – 12p + 32)
= 2p (p – 8) (p – 4)
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 5
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 6

Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4

Question 2.
Find the excluded values , if any of the following expressions.

(i) \(\frac{y}{y^{2}-25}\)
Answer:
The expression \(\frac{y}{y^{2}-25}\) 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

Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4

(ii) \(\frac{t}{t^{2}-5 t+6}\)
Answer:
The expression \(\frac{t}{t^{2}-5 t+6}\) is undefined
when t2 – 5t + 6 = 0
(t – 3) (t – 2) = 0
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 7
t – 3 = 0 or t – 2 = 0
t = 3 or t = 2
The excluded values are 2 and 3

(iii) \(\frac{x^{2}+6 x+8}{x^{2}+x-2}\)
Answer:
x2 + 6x + 8 = (x + 4) (x + 2)
x2 + x – 2 = (x + 2) (x – 1)
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 8
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 9
The expression \(\frac { x+4 }{ x-1 } \) is undefined
when x – 1 = 0
∵ x = 1
The excluded value is 1

Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4

(iv) \(\frac{x^{3}-27}{x^{3}+x^{2}-6 x}\)
x3 – 27 = x3 – 33
= (x – 3) (x2 + x + 3)
x3 + x2 – 6x = x(x2 + x – 6) = x (x + 3) (x – 2)
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 10
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.4 11
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

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