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3 years ago

How would I solve this Rational Equation? Solve for all values of x.

Mathematics

1 answer:

Nesterboy [21]3 years ago

4 0

9514 1404 393

Answer:

x = 4

Step-by-step explanation:

I like to put these in the form f(x) = 0. We can do that by subtracting the right side. Common factors can be cancelled from numerator and denominator, provided they are not zero.

$\dfrac{7}{x+3}+\dfrac{3}{x-3}-\dfrac{x}{x-3}=0\\\\ \dfrac{7(x-3)+(x+3)(3-x)}{(x+3)(x-3)}=0\\\\\dfrac{(x-3)(4-x)}{(x-3)(x+3)}=0\\\\ \dfrac{4-x}{x+3}=0\qquad x\ne3\\\\x=4 \qquad\text{equate the numerator to zero, add $x$}$

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If you leave the numerator as (x-3)(4-x), then there are two values of x that make it zero. Because x=3 makes the equation "undefined", it cannot be considered to be a solution.

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2 years ago

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Thus, options A and D hold, from the simplifications above.

Let's consider the validity of the remaining options provided.

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Hence, the correct options that apply are options A, D, E and F

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10 months ago

A club has 800 members. 100 of the members were randomly picked and were asked if the dues should be raised. 6 of the members sa

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Answer:

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Step-by-step explanation:

Here, we shall be using a case of a representative sampling to determine the actual.

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