Part 10

7. 2x^2 - x - 15, 3x^2 - 11x + 6, 2x^3 - x^2 - 13x - 6. (College Entrance Board.)

8. (tv - v^2)^3, v^3 - t^2v, t^3 - v^3, v^2 - 2vt + t^2.

Pick out the H. C. F. and the L. C. M. of the following:

9. 8(x^2 + y)^(32) (t^2 + z)^(19) (m - n^3)^(14), 12(x^2 + y)^(23) (t^2 + z)^(41) (m - n^3)^(17), 18(m - n^3)^(11) (x^2 + y)^(39) (t^2 + z)^(37).

10. 17ax^3 (y + z)^(10) (y - x)^(19) (x + z)^(27), 34a^2 x^4 (y + z)^(11) (y - x)^(21) (x + z)^(13), 51a^3 x^5 (y + z)^4 (x + z)^(32) (y - x)^(29).

~Reference:~ The chapter on H. C. F. and L. C. M. in any algebra.

FRACTIONS

Define: fraction, terms of a fraction, reciprocal of a number.

Look up the law of signs as it applies to fractions. Except for this, fractions in algebra are treated exactly the same as they are in arithmetic.

1. Reduce to lowest terms:

(a) 32/24;

(b) (a^6 - x^6)/(a^4 - x^4);

(c) [(a + b)^2 - (c + d)^2]/[(a + c)^2 - (b + d)^2]. (M. I. T.)

2. Reduce to a mixed expression:

(a) 756/11;

(b) (a^3 + b^3)/(a - b).

3. Reduce to an improper fraction:

(a) 45-1/8;

(b) 9-11/12 qt.;

(c) a^2 - ab + b^2 - (b^3)/(a + b).

Add:

4. 5/18 + 7/9 + 11/16 + 5/8.

5. 5/(1 + 2x) - (3x)/(1 - 2x) + (4 - 13x)/(4x^2 - 1).

6. 1/[x(x - a)(x - b)] + 1/[a(a - x)(a - b)] + 1/[b(b - x)(b - a)].

Multiply:

7. 72/121 x 55/56 x 77/90.

8. (b - y)/(a^3 + y^3) x (ca + cy)/(b^2 + by) x (b^6 + y^6)/(b^2 + y^2) x b/c.

Divide: