Simplify expression (5xy^-6/x^4 y^-2)^2

s2008m [1.1K]

Answer:

$\huge\boxed{\dfrac{x^2+9^2}{x-3y}+\dfrac{6xy}{3y-x}=x-3y}$

Step-by-step explanation:

Domain:

$x-3y\neq0\Rightarrow x\neq3y$

$\dfrac{x^2+9y^2}{x-3y}+\dfrac{6xy}{3y-x}=\dfrac{x^2+9y^2}{x-3y}+\dfrac{6xy}{-(x-3y)}\\\\=\dfrac{x^2+9y^2}{x-3y}-\dfrac{6xy}{x-3y}=\dfrac{x^2+9y^2-6xy}{x-3y}\\\\=\dfrac{x^2-2(x)(3y)+(3y)^2}{3y-x}=\dfrac{(x-3y)^2}{3y-x}\\\\=\dfrac{\bigg[-1(3y-x)\bigg]^2}{3y-x}=\dfrac{(-1)^2(3y-x)^2}{3y-x}\\\\=\dfrac{1(x-3y)(x-3y)}{x-3y}=x-3y$

Used:

The distributive property: a(b + c) = ab + ac

(a - b)² = a² - 2ab + b²

6 0

3 years ago

Help again for the last time ;-;

lys-0071 [83]

Answer:

1) Star: (-5,9) 2) Lightning (0,8)

3) Circle: (4,-7) 4) Heart (-3,-8)

5) Cross (6,9) 6) Triangle (0,6)

7) Moon (-4,9) 8) Square (-4,6)

9) Diamond (-1,-4) 10) Music Note (8,1)

Step-by-step explanation:

The way that I solved this was I first set up (x,y). You must find the placement of the x-axis or the horizontal line. Then you find the 7-axis or the vertical line. For example, with the star, the shape is 5 to the left which is -5 and then goes 9 lines upward.

7 0

3 years ago

Mr.wilson wrote the fuction f(x)=7x-15 on the chalkboard.What is the value of this function for f(6)?

bixtya [17]

By plunging 5 into the equation as x, you have the equation

7(5) - 15

7 * 5 = 35 so

35 - 15

f(5) = 20

4 0

3 years ago

What is a ratio? (In your own words,don't get off internet.)

mars1129 [50]

Answer:

a ratio is a rate is something left to right like a book so say if a Problem say there's a rate 14 boys to 12 girls then he says rate girls to boys then it would be 12:14 or 12 to 14

Step-by-step explanation:

Please give me brainlyest.

6 0

3 years ago

Read 2 more answers

If the sum of first n terms of an AP is 3n² + 5n find the AP.

ollegr [7]

Let a (n) denote the n-th term in the progression. Consecutive terms in the sequence differ by a fixed constant - call it c - such that

a (n) = a (n - 1) + c

Let a = a (1) be the first term in the sequence. We can solve for a (n) in terms of a alone:

a (n) = a (n - 1) + c

a (n) = (a (n - 2) + c) + c = a (n - 2) + 2c

a (n) = (a (n - 3) + c) + c = a (n - 3) + 3c

and so on, down to

a (n) = a + (n - 1) c

The sum of the first n terms is then

$\displaystyle\sum_{k=1}^n a(k)=\sum_{k=1}^n(a+(k-1)c)=a\sum_{k=1}^n1+c\sum_{k=1}^n(k-1)=an+\frac{cn(n-1)}2=\frac c2n^2+\left(a-\frac c2\right)n$

Since this is equal to 3n ^2 + 5n, it follows that

c/2 = 3 => c = 6

a - c/2 = 5 => a = 8

So the sequence is

a (n) = 8 + (n - 1) 6 = 6n + 2

3 0

3 years ago