StudentAidUnit 5: Algebraic Fractions — Exercise 5 1
10th Class Mathematics · Unit 5: Algebraic Fractions
5.1.1.(i) Reduce to lowest terms: (3a^2 - 6ab) / (2a^2b - 4ab^2) (ii) Reduce to lowest terms: (abx + bx^2) / (acx + cx^2) (iii) Reduce to lowest terms: ac / (a^2x^2 - ax) (iv) Reduce to lowest terms: 15a^2b^2c / [100(a^2 - a^2b)] (v) Reduce to lowest terms: (4x^2 - 9y^2) / (4x^2 + 6xy) (vi) Reduce to lowest terms: 20(x^3 - y^3) / (5x^2 + 5xy + 5y^2) (vii) Reduce to lowest terms: x(2a^2 - 3ax) / [a(4a^2x - 9x^3)] (viii) Reduce to lowest terms: (x^2 - 5x) / (x^2 - 4x - 5) (ix) Reduce to lowest terms: (3x^2 + 6x) / (x^2 + 4x + 4) (x) Reduce to lowest terms: (x^2 + xy - 2y^2) / (x^3 - y^3) (xi) Reduce to lowest terms: (2x^2 + 17x + 21) / (3x^2 + 26x + 35)
(i) Factor
3a2-6ab2a2b-4ab2 = 3a(a-2b)2ab(a-2b)
(i) Cancel (a-2b)
= 3a2ab
Result
(i)
= 32b
(ii) Factor
abx+bx2acx+cx2 = bx(a+x)cx(a+x)
(ii)
= bc
(iii) Factor denominator
aca2x2-ax = acax(ax-1)
(iii)
= cx(ax-1)
(iv) Factor denominator
15a2b2c100(a2-a2b) = 15a2b2c100a2(1-b)
(iv) Cancel a^2
= 15b2c100(1-b)
(iv)
= 3b2c20(1-b)
(v) Factor
4x2-9y24x2+6xy = (2x-3y)(2x+3y)2x(2x+3y)
(v)
= 2x-3y2x
(vi) Factor
20(x3-y3)5x2+5xy+5y2 = 20(x-y)(x2+xy+y2)5(x2+xy+y2)
(vi)
= 4(x-y)
(vii) Factor
x(2a2-3ax)a(4a2x-9x3) = x · a(2a-3x)a · x(2a-3x)(2a+3x)
(vii)
= 12a+3x
(viii) Factor
x2-5xx2-4x-5 = x(x-5)(x-5)(x+1)
(viii)
= xx+1
(ix) Factor
3x2+6xx2+4x+4 = 3x(x+2)(x+2)2
(ix)
= 3xx+2
(x) Factor
x2+xy-2y2x3-y3 = (x+2y)(x-y)(x-y)(x2+xy+y2)
(x)
= x+2yx2+xy+y2
(xi) Factor
2x2+17x+213x2+26x+35 = (2x+3)(x+7)(3x+5)(x+7)
(xi)
= 2x+33x+5