☰ Contents · Algebra

Chapter V review

Lessons 34 · 1 lessons · Sh.A. Alimov, O.R. Xolmuhamedov, M.A. Mirzaahmedov. Algebra, Grade 7, revised and expanded 5th edition. O‘qituvchi NMIU, Tashkent, 2017
34

Chapter V review exercises

Textbook: pp. 150–153
GoalReview the algebraic fractions of Chapter V and solve mixed exercises.
New words
admissible values · joiz qiymatlarreducing · qisqartirishcommon denominator · umumiy maxrajreciprocal fraction · teskari kasr
Explanation

In Chapter V we studied the algebraic fraction, its admissible values and basic property, reducing, bringing to a common denominator, addition, subtraction, multiplication, division and combined operations. In every task the following order is useful: 1) factor the denominators and note the admissible values; 2) for addition and subtraction, bring to a common denominator; 3) for multiplication and division, multiply by the reciprocal and cancel; 4) reduce the result and write it in standard form. The factoring skill from Chapter IV is crucial when working with fractions. The result can also be checked by substituting a value.

Worked examples
((a² - b²)/(a² + ab)) : ((a - b)/a²) = ((a - b)(a + b)/(a(a + b))) · (a²/(a - b)) = a.
1/(x - 1) - 1/(x + 1) = ((x + 1) - (x - 1))/((x - 1)(x + 1)) = 2/(x² - 1).
Class activity

“Fraction olympiad”: teams solve 5 tasks (reducing, adding, multiplying, dividing, mixed) against the clock. Each correct answer scores a point, each mistake costs one.

Practice
1
Reduce (x² - 6x + 9)/(x² - 9).
2
Simplify 1/(x - 1) - 1/(x + 1).
3
Find the value of (x + 3)/(x - 3) at x = 9.
4
Why must we note x ≠ 1 and x ≠ -1 for 1/(x - 1) - 1/(x + 1)?