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How do you solve rational equations #1/2 + 1/4 = 1/x#?

Answer 1

Kennedy Adams

# x = 4/3 #

first thing to do is simplify the left hand side of the equation by adding the fractions.

# 1/2 + 1/4 = 2/4 + 1/4 = 3/4 #

#rArr 3/4 = 1/x #

and cross-multiplying gives 3x = 4

now divide both sides by 3

# rArr x = 4/3 #

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Answer 2

Julia Adams

To solve the rational equation 1/2 + 1/4 = 1/x, we need to find the value of x that satisfies the equation.

First, we need to find a common denominator for the fractions on the left side of the equation. The least common denominator (LCD) for 2 and 4 is 4.

Next, we rewrite the fractions with the LCD of 4: 2/4 + 1/4 = 1/x.

Combining the fractions on the left side gives us 3/4 = 1/x.

To isolate x, we can cross-multiply: 3x = 4.

Finally, we solve for x by dividing both sides of the equation by 3: x = 4/3.

Therefore, the solution to the rational equation 1/2 + 1/4 = 1/x is x = 4/3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.