All categories

3 years ago

Simplify 16x^2 9y^2/(4x-3y)^2

Mathematics

1 answer:

Brrunno [24]3 years ago

4 0

Hey There!!

STEP 1:

Simplify ——————————

(4x + 3y)2

Equation at the end of step

(4x-3y) 1

——————————————————————————— ÷ ————————

(((16•(x2))+24xy)+(9•(y2))) (4x+3y)2

STEP 2:

Equation at the end of step

(4x-3y) 1

——————————————————————— ÷ ————————

(((16•(x2))+24xy)+32y2) (4x+3y)2

STEP 3:

Equation at the end of step

(4x - 3y) 1

—————————————————————— ÷ ——————————

((24x2 + 24xy) + 32y2) (4x + 3y)2

STEP 4:

4x - 3y

Simplify —————————————————

16x2 + 24xy + 9y2

Trying to factor a multi variable polynomial :

4.1 Factoring 16x2 + 24xy + 9y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (4x + 3y)•(4x + 3y)

Detecting a perfect square :

4.2 16x2 +24xy +9y2 is a perfect square

It factors into (4x+3y)•(4x+3y)

which is another way of writing (4x+3y)2

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Equation at the end of step

(4x - 3y) 1

—————————— ÷ ——————————

(4x + 3y)2 (4x + 3y)2

STEP 5:

4x-3y 1

Divide ———————— by ————————

(4x+3y)2 (4x+3y)2

5.1 Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

4x - 3y 1 4x - 3y (4x + 3y)2

—————————— ÷ —————————— = —————————— • ——————————

(4x + 3y)2 (4x + 3y)2 (4x + 3y)2 1

Canceling Out :

5.2 Cancel out (4x + 3y)2 which appears on both sides of the fraction line.

Final result :

4x - 3y

Hope It Helped!~ ♡

ItsNobody~ ☆

You might be interested in

The mean is affected by outliers

Vlad1618 [11]

Yes it is :)

If there is an outlier on the lower end of the graph the mean will go down. If there is an outlier at the higher end of the graph the mean will go up.

8 0

3 years ago

The velocity of a particle moving back and forth on a line is vequalsStartFraction ds Over dt EndFraction equals6 sine (2 t )Sta

max2010maxim [7]

Answer:

s = 6 m

Step-by-step explanation:

The value of the velocity v is given as:

$v = \frac{ds}{dt} = 6 sin(2t)$ m/s

To find s, we have to integrate and apply the initial values of s = o when t = 0:

$\frac{ds}{dt} = 6 sin(2t)\\\\\int\limits^s_0 {ds} = \int\limits^t_0 {6sin(2t)} \, dt\\\\s|^s_o = -3cos(2t)|^t_o\\\\s - 0 = -3cos(2t) -(-3cos(0))\\\\s = -3cos(2t) + 3(1)\\\\s = -3cos(2t) + 3$

When t = π/2, s will be:

s = -3cos(2 * π/2) + 3

s = -3cos(π) + 3

s = -3(-1) + 3

s = 3 + 3

s = 6 m

4 0

4 years ago

In the triangle below, suppose that m < K = (5x - 3) degrees, m < L = (6x - 9) degrees, and m < M = x degree.

MakcuM [25]

Answer:

x = 16

angle K = 77

angle L = 87

angle M = 16

Step-by-step explanation:

Mathematically, the sum of interior angles of a triangle is 180 degrees

Thus:

(5x-3) + (6x-9) + x =180

12x -12 = 180

12x = 180+12

12x = 192

x = 192/12

x = 16

Angle K = 5x-3 = 5(16)-3 = 80-3 = 77

Angle L = 6(16)-9 = 96-9 = 87

Lastly;

angle M = 16 degrees

4 0

3 years ago

PLEASE HELP!

tekilochka [14]

Solve for x over the real numbers:x^3 = 1/27
Hint: | Eliminate the power on the left-hand side.Take cube roots of both sides:Answer: x = 1/3

6 0

4 years ago

Read 2 more answers

Of the following fractions ,which is less than2/3 following fraction include 7/8,5/6,9/

fredd [130]

3/5 into a percent is 60 is is less than 2/3 as a percent of 66.66

5 0

4 years ago

Simplify 16x^2 9y^2/(4x-3y)^2​

Simplify 16x^2 9y^2/(4x-3y)^2