Math Problem Statement

Hitunglah hasil operasi aljabar berikut: 1. (a) (3 / 2x) × (2x / 3), (b) (y - 5) / y × (2 + 3y) / (y - 3), (c) (a^3b^2) / (a^5b), (d) (1 / (x + y)) × (3 / (x - y)); 2. Tunjukkan bahwa x - 1 ekuivalen dengan 1/2 (2x - 2).

Solution

The image contains mathematical operations and algebraic expressions that need to be solved. Let's break down the questions:

Question 1: Hitunglah hasil operasi aljabar berikut!

Solve the following algebraic operations:

a) 32x×2x3\frac{3}{2x} \times \frac{2x}{3}

b) y5y×2+3yy3\frac{y-5}{y} \times \frac{2+3y}{y-3}

c) a3b2a5b\frac{a^3b^2}{a^5b}

d) 1x+y×3xy\frac{1}{x+y} \times \frac{3}{x-y}

Question 2: Tunjukkan bahwa x1x - 1 ekuivalen dengan 12(2x2)\frac{1}{2} (2x - 2)

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Expressions
Fraction Operations

Formulas

Multiplication of fractions: (a/b) × (c/d) = (a × c) / (b × d)
Laws of exponents: a^m / a^n = a^(m-n)

Theorems

Distributive property: a(b + c) = ab + ac
Basic properties of equivalence in algebra

Suitable Grade Level

Grades 8-10