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.
\left(2a-b\right)^2\:\div \frac{4a^3-ab^2}{3}
find domain
7 answers
find domain
4y/3x^2+2xy - 9x/3xy+2y^2
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.
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.
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 $3x+2y = 0$.
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 $3x+2y = 0$.
1 answer