Rational Algebraic Expressions Objective: To simplify rational algebraic expressions.
Unit# 4 Algebraic Expressions and Algebraic Formulas Exercise 4.1
16
Mudassar Nazar Notes Published by Asghar Ali Page 1 Unit# 4 Algebraic Expression and Algebraic Formulas Exercise 4.1 Question # 3 Reduce the following rational expressions to the lowest form: (iv) . Solution . = = = = (v) Solution =
-
Upload
asghar-ali -
Category
Documents
-
view
273 -
download
1
Transcript of Unit# 4 Algebraic Expressions and Algebraic Formulas Exercise 4.1
Mudassar Nazar Notes Published by Asghar Ali Page 1
Unit# 4 Algebraic Expression and Algebraic Formulas
Exercise 4.1
Question # 3 Reduce the following rational expressions to the lowest form:
(iv) .
Solution
.
=
=
=
=
(v)
Solution
=
Mudassar Nazar Notes Published by Asghar Ali Page 2
=
=
(vi)
Solution
=
=
=
=
(vii)
Solution
=
Mudassar Nazar Notes Published by Asghar Ali Page 3
=
=
=
=
= 4x ( x – 1 )
(viii)
Solution
=
=
=
=
= x2 + 3x – 4
Mudassar Nazar Notes Published by Asghar Ali Page 4
Question # 5 Perform the indicated operation and simplify:
(iv) - -
Solution
- -
=
=
=
=
=
(v) -
Solution
-
= -
= -
= -
Mudassar Nazar Notes Published by Asghar Ali Page 5
=
=
=
=
=
(vi) - - -
Solution
- - -
= [ - ] – [ - ]
= – [ ]
= [ ] - [ ]
= -
=
=
=
Mudassar Nazar Notes Published by Asghar Ali Page 6
Exercise 4.4
Question # 1
Rationalize the denominator of the following:
(i)
Solution
=
=
=
=
(ii)
Solution
=
=
=
Mudassar Nazar Notes Published by Asghar Ali Page 7
=
=
=
=
(iii)
Solution
=
=
=
=
=
=
Mudassar Nazar Notes Published by Asghar Ali Page 8
(iv)
Solution
=
=
=
=
=
= ( 3 -2 )
(v)
Solution
=
=
=
=
= + 4
Mudassar Nazar Notes Published by Asghar Ali Page 9
(vi)
Solution
=
=
=
=
= +
(vii)
Solution
=
=
=
Mudassar Nazar Notes Published by Asghar Ali Page 10
=
=
=
=
=
=
(viii)
Solution
=
=
=
=
=
Mudassar Nazar Notes Published by Asghar Ali Page 11
=
=
=
=
Question # 3
If x + = 3, find (i) x2 + , (ii) x4 +
Solution
x + = 3
(x + )2 = (3)2
x2 + + 2 = 9
x2 + = 9 – 2
x2 + = 7
(x2 + )2 = (7)2
X4 + + 2 = 49
X4 + = 49 – 2
X4 + = 47
Mudassar Nazar Notes Published by Asghar Ali Page 12
Question # 4
If x - = 2, find (i) x2 + , (ii) x4 +
Solution
x - = 2
(x - )2 = (2)2
x2 + - 2 = 4
x2 + = 4 + 2
x2 + = 6
(x2 + )2 = (6)2
X4 + + 2 = 36
X4 + = 36 - 2
X4 + = 34
Question # 5
(ii) If x = , find the value of x + , and
Solution
x =
Mudassar Nazar Notes Published by Asghar Ali Page 13
=
x + = +
x + =
x + =
x + =
x + =
x + =
x + =
(x + )2 =( )2
x2 + + 2 =
x2 + = – 2
x2 + =
x2 + =
(x + )3 =( )3
x3 + + 3(x + ) =
x3 + + 3( ) =
Mudassar Nazar Notes Published by Asghar Ali Page 14
x3 + + 14 =
x3 + = - 14
x3 + =
x3 + =
Question # 6
If p = 2+ , find (i) p + , (ii) p - , (iii) p2 +
Solution
p = 2+
=
=
=
=
=
= 2 -
(i) p + = 2 + + 2 -
p + = 4
(ii) p - = 2 + - ( 2 - )
Mudassar Nazar Notes Published by Asghar Ali Page 15
p - = 2 + + 2 +
p - = 2
(iii) (p + )2 = (4)2
P2 + + 2 = 16
P2 + = 16 – 2
P2 + = 14
(iv) P2 - = (p + ) (p - )
P2 - = (4) (2 )
P2 - =
Question # 7
If q = + 2, find (i) q + , (ii) q - , (iii) q2+ , (iv) q2-
Solution
q = + 2
=
=
=
=
Mudassar Nazar Notes Published by Asghar Ali Page 16
=
=
(i) q + = +
q + = 2
(ii) q - = -( )
q - = -
q - = 4
(iii) (q + )2 = (2 )2
q2+ + 2 = 4 5
q2+ + 2 = 20
q2+ = 20 – 2
q2+ = 18
(iv) q2- = (q + ) (q - )
q2- = ) (4)
q2- = 8
