Mathematics, 27.07.2019 14:30 Tyrant4life

Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81 times quantity x squared plus 12 x plus 36 over quantity x plus 6. quantity x plus 6 over quantity x minus 9 the quantity x plus 6 end quantity over the quantity x minus 9 end quantity squared. the quantity x plus 6 end quantity squared over the quantity x minus 9 the quantity x plus 6 end quantity squared over the quantity x minus 9 end quantity squared.

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Answer from: haileygrace2282

$\frac{x-6}{x-9}$

Step-by-step explanation:

The given expression is

$x^{2} -3x-54 \div x^{2} -18x+81$

To solve this division, we could find the solution factors of each expression.

So, let's work on the numerator first

$x^{2} -3x-54$

First, we need to express this in two factors, where the sign of the first factor would be the same as the second term of the given expression (negative). And the sign of the second factor would be the product of the sign of the second factor term and the third term. As follows

$x^{2} -3x-54=(x-a)(x+b)$

So, and would be two number which product is 54 and its subtraction is 3. You would find that 9 and 6 are those number because

$9 \times 6 = 54\\9 - 6 =3$

Therefore, the solution factors are

$x^{2} -3x-54=(x-9)(x+6)$

Then, we do the same process with the denominator

$x^{2} -18x+81=(x-9)(x-9)$

In this case, we needed to find to number which product is 81 and which sum is 18.

Now, we replace all these factor into the given fraction.

$x^{2} -3x-54 \div x^{2} -18x+81=\frac{(x-9)(x+6)}{(x-9)(x-9)} =\frac{x-6}{x-9}$

Therefore, most simple form of the given expression is

$\frac{x-6}{x-9}$

Answer from: Quest

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Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81...

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