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You have the right idea that things need to get multiplied.
What should be done is that the entire fraction needs to get multipled by the lowest common denominator of both denominators.
Let's look at the complex numerator. Its denominators are 5 and x + 6. Nothing is common with these, so both pieces are needed.
The complex denominator has x - 3 as its denominator. With nothing in common between it and the complex numerator, that piece is needed.
So we multiply the entire complex fraction by (5)(x + 6)(x -3).
Numerator:
= (x+6)(x-3) - (5)(5)(x-3)
= (x+6)(x-3) - 25(x-3)
= (x-3)(x + 6 - 25) <--- by group factoring the common x - 3
= (x -3)(x - 19)
Denominator:
Now we put the pieces together.
Our fraction simplies to (x - 3) (x - 19) / 125 (x + 6)
The value of the variable is 4√5. Then the correct option is C.
<h3>What is the triangle?</h3>A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The similar triangles are shown in the diagram.
16 / x = x / 5
x² = 16 × 5
x = 4 √5
Then the value of the variable is 4√5.
Then the correct option is C.
More about the triangle link is given below.
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