Solve each equation. Leave your answer as a fraction if it...

Key Concepts

Clearing Fractions

Clearing fractions often involves multiplying both sides of an equation by the denominator to eliminate the fractional coefficients. This simplifies the equation and makes it easier to isolate the variable and solve for its value.

Linear Equations

Linear equations involve expressions where the variable is raised only to the first power, and solving them requires isolating the variable through a series of algebraic steps. Mastering linear equations is fundamental in algebra as it forms the basis for solving more complex equations and systems of equations.

Isolation of Variables

Isolating the variable means manipulating the equation using algebraic operations (addition, subtraction, multiplication, division) to get the variable on one side of the equation and the constants on the other. This process is crucial to finding the value of the variable in a clear and systematic way.

Inverse Operations

Inverse operations are the mathematical operations that undo each other, such as addition and subtraction or multiplication and division. They are essential in solving equations because they allow one to reverse operations applied to the variable, thereby isolating and determining its value.

Transcript

00:01 This question asks to solve the following equation.

00:04 As you can see, the variable x is in denominator and in two fractions.

00:11 So let's make the denominator equal of these two fractions in order to be able to add them.

00:18 So this is, in other words, multiplying this fraction by x plus 1, multiply the denominator by x plus 1, multiply the denominator by x plus 1, and for this fraction, multiply the numerator by x plus 1, and the denominator by x.

00:31 X so this is 3 multiplied by x plus 1 plus 4 multiplied by x over the common denominator which is x multiplied by x plus 1 equals to 2 now i don't want this to be in the denominator so i multiply both sides by x multiplied by x plus 1 so both sides will be multiplied by x plus 1 this is multiple by x plus 1 this is multiplied by x x plus 1 and hence then this will be cancelled this is by distributing 3 inside the brackets becomes 3x plus 3 plus 4x equals to the right hand side where x can be distributed also inside the brackets or 2x can with 2 as well so it's 2x multiplied by x which is 2x4 of 2 plus 2 multiply x multiplied by 1 is 2x.

01:49 Now let's arrange these terms.

01:51 I want them all to be in one side.

01:53 So i'll shift the 2x squared to the other side and 2x as well to the other side.

02:01 So they become negative in the other side of the equation.

02:06 So this is minus 2x 4f2 minus 2x.

02:13 Plus 3x plus 3 plus 4x equals the right hand side now becomes 0.

02:24 Now let's add the common terms minus 2x squared.

02:28 There is no other term which has x4 .2.

02:33 These 3 can be added.

02:37 Minus 2x plus 3x is 1x and plus 4x will be 5x and plus 3x will be 5x and plus 3x.

02:47 3 equals to 0.

02:50 So i got now a quality equation.