(a+b)(a+b)=a2+2ab+b2) a2+2ab+b2—a2+2ab—b2

(a—b) (a—b)—a2—2ab+b2

4ab

a2-b2

The fractions reduced to 2x 5х 2xX7 5x X5 +

a common denominator.
14x 25x 39x

+

3x X5

2ax

15x

Here +

+

+

6x 13x

Here

+

5' 7 5X7 5X7 35 35 35

3x
2aXx
Х
2a 5 2aX5 2aX5 10a 10a

X x x 12x 8.x

+o+
2 3 4 24

+24+24 Ans.

12

Here these fractions may be written thus; 2a + 3a +a+

Ans.

MULTIPLICATION OF ALGEBRAIC FRACTIONS.

52. RULE. Multiply all the numerators together for the numerator of the product, and all the denominators together for its denominator; the former placed over the latter will give the product required.

2x 3x 3x 5x

2x

1. Multiply by or by or by

2' 2 36'

2xX3x 6x2 3x2 5xx3x 5X2a 10a 5a' 2X3b

or

15x2 2x X3x

or 9

3x

7

6x2

26 7(x-1) 7x-7'

3ax-5a 3x2(15x-30) 3x2X3 922 9x

or

4x2-6

2x(5x-10)

2x 2

15x-30

2x

Ans.

4x2-8x 2xX3xX5x 302 15x3

2x

(x-2)4x

or

Ans.

4a3—8a1x+16a3x3—5a2x2+2a3x+2ax3+8ax1—4x3

53. RULE. Invert the divisor, and then proceed as in Multiplication.

(x2+b2) (x2—b2)

(x2-b2)Xx

5a1-5b*

6a2+5ab

(x2+b2) (x2—b2) (x—b)

(x—b) (x—b) (x+b) Xx

4. Divide

or

x2 + xy by by x-y (x-y)2 2a2-4ab+262 4a-4b (x2+xy) (x2-2xy+y2) (x2+xy) (xy) x2+xy=x(x+y)

(x-y) (xy)

5a1 564 4ab2b2 (5X2) (a*b1)

2a2

(a—b) (6a2+5ab)

3x 11

12

x23+x2y+xy2+y3° 6a2 + 5ab (5a5b') X (4a-46)

4a 46 (2a2-4ab-2b2) (6a2+5ab 5.2.(a3+a2b+ab2+b3 ___ 10 (a3+a2b+ab2+b3

5. Divide by or 4

11 3x 12 9x 622 3x

X

6x2
5

by 3x, or

3x+1 4x
by or

9

3 2x-1

by 3.

A.

- or

=

12 4 11 11 5 1

4x 3a Za-b
by or

6x2 1 2x
X
5 3x 5

3x

4

6. Divide

5 56

4cd

Бас

10ac2