 ### Algebraic Fractions

Algebraic Fractions What is an algebraic fraction? An algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. We will explain some techniques to simplify complex algebraic fractions. We know that we can simplify fractions by dividing the numerator and denominator by a common factor. This can also be done with algebraic fractions. Example […] ### Linear Inequalities

Linear inequalities Number lines Suppose that you are told that x<4. This means that each possible value of x must be less than 4. Therefore, x can be 3, 2, 1, 0, -1, -2…….but that is not all. 3.2 is also less than 4, as is 3.999, 2.43, -3.4, -100…….. If we draw a number […] Rearrengement of a formula Very often you will find that a formula is expressed with one variable written alone in one side of the ‘=’ symbol (usually on the left but not always). The variable that is written alone is known as the subject of the formula. Consider each of the following formulas $displaystyle s=ut+frac{1}{2}a{{t}^{2}}$   ($[…] ### Dividing Polynomial Expressions By Math Original No comments Dividing Polynomial Expressions What is a Polynomial? A polynomial is an expression obtained when we add or subtract two or more monomials. Dividing Polynomials Dividing polynomials with monomial expression is easy, all you have to do is divide each term of the polynomial by the monomial. Example 1: Dividing$displaystyle {10x+5}$by$displaystyle 5$.$displaystyle frac{{10x+5}}{5}=frac{{10x}}{5}+frac{5}{5}=2x+1$Example 2 :Dividing$displaystyle frac{{12{{x}^{2}}+8x+20}}{{4x}}=$[…] ### Rules of Roots By Math Original No comments Rules of Roots What is the nth root? The number that must be multiplied itself n times to equal a given value. The nth root of x is written$ displaystyle sqrt[n]{x}$or$ displaystyle {{x}^{{frac{1}{n}}}}$. The rules below are a subset of the rules of exponents, because roots are the inverse operations of exponentiation. Definitions […] ### Rules of Exponents By Math Original No comments Rules of Exponents Zero-Exponent Rule:$displaystyle {{a}^{0}}=1$this means that each number raised to the zero power is 1. Worked example 1: 50 = 1 (-3)0 = 1$displaystyle {{(5{{x}^{6}}{{y}^{2}})}^{0}}=1displaystyle {{left( frac{2}{x} right)}^{0}}=1$Power of a Power:$displaystyle {{left( {{a}^{m}} right)}^{n}}={{a}^{mn}}$So, when you raise a power to a power you have to multiply the exponents. Worked example 2: […] ### Logarithm By Math Original No comments Logarithm Logarithm PropertiesThere is a close relationship between logarithms and exponents. The logarithm of a number is defined as the power or index to which a given base must be raised to obtain the number. If we have$ displaystyle {{a}^{x}}=M$where a and M are greater than zero and a≠1 then we can write this in a logarithm […] ### Worked Examples – Quadratic Equations By Math Original No comments Worked Examples – Quadratic equation Methods to solve a quadratic equation are: Square Root Method Quadratic FormulaFactoring Completing the square Graphing We have four types of quadratic equations 1. Quadratic equations in the standard form$ displaystyle a{{x}^{2}}+bx+c=0$We can solve them by using the quadratic formula, graphing or factoring and completing the square. 2. Quadratic […] ### Combining Functions By Math Original No comments Combining Functions Combining Functions means performing basic arithmetic operations like addition, subtraction, multiplication and division with functions. Given two functions$ displaystyle f(x)$and$ displaystyle g(x)$we define: 1. The sum of two functions$displaystyle (f+g)(x)=f(x)+g(x)$2. The difference of two functions$ displaystyle (f-g)(x)=f(x)-g(x)$3. The product of two functions$ displaystyle (ftimes […] 