Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3

Mathematics

1 answer:

dezoksy [38]3 years ago

4 0

Answer:

Step-by-step explanation:

4/x + 4/(x²-9) = 3/(x - 3)

4 / x + 4 / [( x - 3) ( x + 3 )] = 3 / ( x - 3 ) / * x ( x - 3 ) ( x + 3 )

Restrictions : x ≠ 0, x ≠ - 3 , x ≠ 3;

4 ( x + 3 ) ( x - 3 ) + 4 x = 3 x ( x + 3 )

4 ( x² - 9 ) + 4 x = 3 x² + 9 x

4 x² - 36 + 4 x - 3 x² - 9 x = 0

x² - 5 x - 36 = 0

x² - 9 x + 4 x - 36 = 0

x ( x - 9 ) + 4 ( x - 9 ) = 0

( x - 9 ) ( x + 4 ) = 0

x - 9 = 0, or : x + 4 = 0

Answer:

x = 9, x = - 4

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Nat2105 [25]

<h3>Answer: Third choice. $\overline{AC} \perp \overline{BD}$ </h3>

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Explanation:

SAS stands for Side Angle Side. Note how the angle is between the two sides. To prove the triangles congruent with SAS, we need to know two sides and an angle between them.

We already see that BC = CD as shown by the tickmarks. Another pair of sides is AC = AC through the reflexive theorem.

The missing info is the angle measures of ACB and ACD. If we knew those angles were the same, then we could use SAS to prove triangle ACB is congruent to triangle ACD.

It turns out that the angles are congruent only when they are 90 degrees each, leading to AC being perpendicular to BD. We write this as $\overline{AC} \perp \overline {BD}$ . The upside down T symbol meaning "perpendicular" or "the two segments form a right angle".