\left(2a-b\right)^2\:\div \frac{4a^3-ab^2}{3}

find domain

7 answers

The domain of a fraction is restricted by the denominator because division by zero is undefined. Therefore, we only need to consider the denominator of the fraction, which is $4a^3-ab^2$.

To find the domain, we need to determine the values of $a$ and $b$ that make the denominator equal to zero.

Setting the denominator equal to zero:
$4a^3-ab^2 = 0$

Factoring out an $a$:
$a(4a^2-b^2) = 0$

Using the difference of squares formula to factor further:
$a(2a+b)(2a-b) = 0$

Now we have three factors that could equal zero: $a$, $2a+b$, and $2a-b$.

Therefore, the domain is all values of $a$ and $b$ that do not make any of these factors equal to zero.
find domain
4y/3x^2+2xy - 9x/3xy+2y^2
To find the domain of the given expression, we need to determine the values of $x$ and $y$ that make the denominator of each fraction equal to zero.

Let's start by analyzing the first fraction: $\frac{4y}{3x^2+2xy}$.

The denominator is $3x^2+2xy$. Setting it equal to zero:

$3x^2+2xy = 0$

Factoring out an $x$:

$x(3x+2y) = 0$

This equation tells us that either $x = 0$ or $3x+2y = 0$.

Next, let's analyze the second fraction: $-\frac{9x}{3xy+2y^2}$.

The denominator is $3xy+2y^2$. Setting it equal to zero:

$3xy+2y^2 = 0$

Factoring out a $y$:

$y(3x+2y) = 0$

This equation tells us that either $y = 0$ or $3x+2y = 0$.

Now, let's combine the results from both fractions:

Either $x = 0$ or $3x+2y = 0$ (from the first fraction).

Either $y = 0$ or $3x+2y = 0$ (from the second fraction).

Thus, the domain of the expression is all values of $x$ and $y$ that do not make any of these conditions true.
i do not understanf
I apologize for the confusion. Let's break it down step by step.

The given expression is:
$\frac{4y}{3x^2+2xy} - \frac{9x}{3xy+2y^2}$

To find the domain, we need to determine the values of $x$ and $y$ that make the denominators of each fraction equal to zero.

First, let's look at the denominator of the first fraction: $3x^2+2xy$. Setting it equal to zero:

$3x^2+2xy = 0$

This quadratic equation can be factored as:

$x(3x+2y) = 0$

This equation tells us that either $x = 0$ or $3x+2y = 0$.

Now, let's look at the denominator of the second fraction: $3xy+2y^2$. Setting it equal to zero:

$3xy+2y^2 = 0$

This equation can be factored as:

$y(3x+2y) = 0$

This equation tells us that either $y = 0$ or $3x+2y = 0$.

Combining the results from both fractions, we have the following conditions:

Either $x = 0$ or $3x+2y = 0$

Either $y = 0$ or $3x+2y = 0$

The domain of the expression is all values of $x$ and $y$ that do not make any of these conditions true. In other words, any values of $x$ and $y$ that satisfy $x \neq 0$ and $y \neq 0$, or $3x+2y \neq 0$, will be in the domain.
bro what whats the answer
I apologize for the confusion. Let me provide you with the answer.

The domain of the given expression $\frac{4y}{3x^2+2xy} - \frac{9x}{3xy+2y^2}$ is determined by finding the values of $x$ and $y$ that make the denominators of each fraction equal to zero.

For the first fraction, $3x^2 + 2xy$, the denominator is equal to zero when $x = 0$ or $3x+2y = 0$.

For the second fraction, $3xy + 2y^2$, the denominator is equal to zero when $y = 0$ or $3x+2y = 0$.

Therefore, the domain of the expression is all values of $x$ and $y$ such that $x \neq 0$ and $y\neq 0$, and also such that $3x+2y\neq 0$.

In summary, the domain of the expression is all values of $x$ and $y$ except for when $x = 0$, $y = 0$, or $3x+2y = 0$.