# How to solve linear equations with constants in denominators

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## Solving Rational Equations Solve an equation for x by clearing fractions with multiple steps

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Solving Multi-Step Equations. Learning Objective s. There are some equations that you can solve in your head quickly. You only needed to do one thing to get the answer, divide 6 by 2. Other equations are more complicated.

Solving Rational Equations. Learning Objective s. Equations that contain rational expressions are called rational equations. We can solve these equations using the techniques for performing operations with rational expressions and for solving algebraic equations. One method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable. Since the denominator of each expression is the same, the numerators must be equivalent as well.

Intro Harder Probs Graphs. While adding and subtracting rational expressions can be a royal pain, solving rational equations is generally simpler, even if rational expressions are added within those equations. Note that I'm not saying that solving rational equations is "simple"; I'm only saying that it's simpl er. This is because, as soon as you go from a rational expression that is, something with no "equals" sign in it to a rational equation that is, something with an "equals" sign in the middle , you get a whole different set of tools to work with. In particular, once you have that "equals" sign in the middle, you then have two sides, which means that you can multiply through both of those sides of the equation, and this allows you to get rid of the denominators. Solving Rational Equations.

## Linear equations 4

The best approach to address this type of equation is to eliminate all the denominators using the idea of LCD least common denominator. In this lesson, I want to go over ten 10 worked examples with various levels of difficulty. Here we go! Would it be nice if the denominators are not there? The approach is to find the Least Common Denominator also known Least Common Multiple and use that to multiply both sides of the rational equation. It results in the removal of the denominators, leaving us with regular equations that we already know how to solve such as linear and quadratic.

## Equation with the variable in the denominator

Elementary algebra is one of the main branches of mathematics. Algebra introduces the concept of using variables to represent numbers and defines the rules on how to manipulate equations containing these variables. Variables are important because they allow for the formulation of generalized mathematical laws and allow the introduction of unknown numbers into equations. It is these unknown numbers that are the focus of algebra problems, which usually prompt you to solve for the indicated variable. The "standard" variables in algebra are frequently represented as x and y. Move any constant values from the side of the equation with the variable to the other side of the equals sign. Divide the equation by the coefficient of the variable term.

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A linear equation is any equation that can be written in the form. This form is sometimes called the standard form of a linear equation. Note that most linear equations will not start off in this form. One way to think of these rules is the following. What we do to one side of an equation we have to do to the other side of the equation.

The result of this operation will be a new equation, equivalent to the first, but with no fractions. We changed the problem to one we already knew how to solve! After you clear fractions with the LCD, you will simplify the three variable terms, then isolate the variable. Show Solution. Solution: We want to clear the fractions by multiplying both sides of the equation by the LCD of all the fractions in the equation.

## 3 thoughts on “How to solve linear equations with constants in denominators”

1. Noah S. on said:

Solving Multi-Step Equations

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3. Spencer B. on said:

LINEAR EQUATION - Solve for x in the following equation. Example 1: displaymath Get rid of the denominators by multiplying both sides by 28, the smallest number that 4 Add the x terms and the constants on the left side of the equation.