🧮 algebra

1. **State the problem:** Simplify the rational expression $$\dfrac{x^2 - 7x + 12}{x^2 - 6x + 9}$$ to its lowest terms and determine which values of $$x$$ must be excluded from its

1. State the problem: Simplify the expression $$-9b^2 (a+3b)^{m+2} (2b-4c)^2 + m / 4 (3a+9b)^{2m+2} (b^2 - 2cb)^{2 - m}$$. 2. Factor expressions where possible:

1. Problem: Identify the composite number. - Composite numbers have factors other than 1 and itself.

1. The average of $a,b,$ and $e$ is 16, so $$\frac{a+b+e}{3} = 16 \implies a+b+e = 48.$$ 2. The average of $c,d,$ and $e$ is 26, so $$\frac{c+d+e}{3} = 26 \implies c+d+e = 78.$$

1. **State the problem:** We have a studio apartment costing 64000, divided into labour, materials, and contractor's charges in ratio 12:15:5. 2. **Express individual costs:** Let

1. نبدأ بكتابة مسألة السؤال: لدينا دالة د معرفة على مجال ح ونعلم أن $$3d(x) + d(-x) = x^4 - 2x^2 + 1$$

1. **State the problem:** Simplify the expression $$2x^2(5x^5)$$. 2. **Apply the multiplication rule for exponents:** Multiply the coefficients and add the exponents of like bases.

1. Simplify each expression by distributing and combining like terms. 16. Simplify $2(x^2 + 2) + 3(2x + 3)$:

1. Soddalashtiring: 1) $x^2 + 3x + 2 + (2x^2 - 3x + 2)$

1. The problem presents the inequality $31 > 28$. 2. We need to verify if 31 is indeed greater than 28.

1. Evaluate $2^{-4}$. Recall that $a^{-n} = \frac{1}{a^n}$.

1. **State the problem:** We have three lengths of wood in the ratio $2 : 5 : 7$. The difference between two of them is 30 cm. We want to verify if Kofi's statement that the sum of

1. *مقدمة: تعريف الأعداد النسبية* الأعداد النسبية هي الأعداد التي يمكن كتابتها على شكل \(\frac{a}{b}\) حيث \(a\) و \(b\) عددان صحيحان و \(b \neq 0\).

1. Problem 16: A student scores 10 out of 15 on Part 1 and 4 out of 10 on Part 2. To pass the exam, the student needs at least 54% of the total marks. 2. Calculate total marks obta

1. The problem is to express the fraction \(\frac{1}{2}\) in a clear way. 2. \(\frac{1}{2}\) means one part out of two equal parts.

1. Stating the problem: Simplify the expression $$\frac{(9 \times 3^2)^3}{(3 \times 27)^2}$$. 2. Simplify inside the parentheses.

1. Let's start with the first expression: \(2^7 \times 2^4 \times 2^{-8}\). 2. When multiplying powers with the same base, add the exponents:

1. **Problem (a):** Sundip buys 30 litres of fuel at £1.50 per litre and pays the exact amount using three bank notes of £5, £10, £20, or £50. 2. Calculate the total cost of fuel:

**Problem:** Write Leo's time as a fraction of Eve's time and simplify the fraction.

1. **Stating the problem:** We have a sequence of terms $T_1, T_2, \\ldots, T_6$ given as $0, 4, 8, 12, 0, 16$ respectively. 2. We need to find the smallest index $k$ such that $T_

1. Problem (a): Simplify the expression $4x - 3y + x + 7y$. Step 1: Group like terms.