Equations Involving Fractions

Equations Involving Fractions

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Equations Involving Fractions When solving for an unknown in an equation with fractions, we first determine an equivalent equation without fractions, and then solve for the unknown.

Example

Solve for x:

x 2x – 3 = x + 3 2

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Equations Involving Fractions Step 1: Determine the Lowest Common Denominator (LCD) of the fractions.

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Equations Involving Fractions Step 2: Multiply each term in the equation by the LCD.

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Equations Involving Fractions Step 3: Solve for the unknown.

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Solve the following equation for x:

8x + 2 = 5 x–2

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Restrictions When the denominator of a fraction is zero, the value is said to be undefined.

Example

x 0

is an undefined fraction.

When solving an equation where the unknown is in the denominator, we must restrict the values of the unknown which would cause the equation to be undefined.

Example Slide: 7

5 8–x

Restriction: x ≠ 8

Solve the following equation for x. State your restrictions and check your answer. 3 1 21 – = –1 + 2x x 2x

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Solve the following equation for x: 4x – 3 1 1 = + x–1 x–1 2

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Class Problems:

𝒙 − 𝟓 𝟑𝒙 + 𝟕 𝟐𝒙 − = 𝟑 𝟐 𝟒 𝟏𝟒 𝟑 𝟏𝟑 − = − 𝒙 𝟑𝒙 𝟐𝒙 𝟔𝒙

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