🧮 algebra

1. Problem: Simplify $$\frac{2}{x+1} + \frac{1}{x-2} - \frac{1}{x^2 - 1}$$. 2. Note that $$x^2 - 1 = (x+1)(x-1)$$.

1. Simplify each expression: (a) Simplify $\sqrt[3]{252x^{5}}$: Factor $252 = 2^{2} \times 3^{2} \times 7$ and express as $\sqrt[3]{2^{2} \times 3^{2} \times 7 \times x^{5}}$. This

1. Problem 39: Simplify the expression \[\frac{4 - \frac{9}{x^2}}{2 - \frac{3}{x}}\]. Step 1: Find a common denominator in numerator and denominator separately.

1. Problem 30: Simplify $$\frac{2}{x+1} + \frac{1}{x-2} - \frac{1}{x^2 - 1}$$. - Factor denominator: $$x^2 - 1 = (x-1)(x+1)$$.

1. **State the problem:** We need to compute the value of the fraction $$\frac{50.00698 \times 0.081}{0.0049 \times 0.27}$$ without using a calculator. 2. **Simplify the numerator:

1. Q1 a) Problem statement: Solve the equation $\frac{m}{2}+\frac{m}{3}+3=2+\frac{m}{6}$. 2. Q1 a) Step 1: Get a common denominator of 6 for the rational terms.

1. The problem is to understand the expansion of $n!$ (n factorial). 2. The notation $n!$ means the product of all positive integers from 1 up to $n$.

1. The problem asks to simplify or expand the expression $n!^{1/n}$. 2. First, recall that $n!$ (n factorial) is the product of all positive integers from 1 to $n$: $$n! = 1 \times

1. The problem is to evaluate and explain the logarithmic expression $$\log_4(16^3)$$. 2. Using the power rule of logarithms, $$\log_b(a^c) = c \log_b(a)$$, we rewrite $$\log_4(16^

1. **State the problem:** Show that for all real numbers $x, y, z$, the inequality $$x^2 + y^2 + z^2 \geq xy + yz + zx$$ holds. 2. **Rewrite the inequality:** We want to prove:

1. **State the problem:** Find the domain of the function $$g(x) = p 1 - \sin(x) \tan\left(\frac{x}{2} + \frac{1}{x}\right)$$.\n\n2. **Rewrite the problem:** We want all values of

1. **Problem Statement:** Find the A.M. (Arithmetic Means) between given numbers and solve the arithmetic progression (A.P.) problem. 2. **Arithmetic Mean formula:** The $n$ arithm

1. **State the problem:** Simplify the expression $$-(2a - 2) - (a - b) + (a - 6 + b)$$. 2. **Expand the parentheses considering the minus signs:**

1. **State the problem:** Simplify each radical expression using the given radical laws. 2. **Simplify each radical:**

**Question 1: Simplify using laws of indices** 1.i Simplify $ (b^4)^3 b^{-2} $

1. Stating the problem: Simplify the expression $$ -(2a - 2) - (a - b) + (a - b + b) $$. 2. Remove the parentheses by distributing the negative signs:

1. Stating the problem: Simplify the expression $$(3x - y) - (3y - x) - (x - 2).$$ 2. Remove parentheses by distributing the minus signs:

1. Stating the problem: Factorise the expression $$7 - x^2 + 2(x - \sqrt{7})$$. 2. Expand the expression:

1. The problem is to factorize an expression. However, you have not provided a specific expression to factorize. 2. Please provide the expression you want to factorize so I can sho

1. **Énoncé du problème :** Factoriser une expression algébrique non précisée. 2. Sans expression donnée, je ne peux pas factoriser de manière spécifique.

1. Stating the problem: Simplify the expression $7 - x^2 + 2(x - \sqrt{7})$. 2. Expand the terms: $7 - x^2 + 2x - 2\sqrt{7}$.