Math / Algebra

QuestionDivide. $\frac{9}{6 x^{2}-q} \div \frac{54}{30 x^{2}-5 q}$ $\frac{9}{6 x^{2}-q} \div \frac{54}{30 x^{2}-5 q}=$ $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

What is this asking? We're asked to divide one algebraic fraction by another and then simplify the result. Watch out! Remember, dividing by a fraction is the same as multiplying by its reciprocal.
Also, be careful when factoring and simplifying; it's easy to make mistakes with signs and coefficients!

STEP 2

1. Rewrite as Multiplication
2. Factor the Expressions
3. Simplify the Expression

STEP 3

Remember, dividing by a fraction is the same as multiplying by its reciprocal, or "flip and multiply." So, let's flip the second fraction and change the division to multiplication: $\frac{9}{6x^2 - q} \div \frac{54}{30x^2 - 5q} = \frac{9}{6x^2 - q} \cdot \frac{30x^2 - 5q}{54}$

STEP 4

Look at the numerator of the second fraction, $30x^2 - 5q$ .
We can factor out a 5, giving us $5(6x^2 - q)$ .
This is great because we have a similar expression in the denominator of the first fraction!
Our expression now looks like: $\frac{9}{6x^2 - q} \cdot \frac{5(6x^2 - q)}{54}$

STEP 5

Notice how $(6x^2 - q)$ appears in both the numerator and the denominator.
We can divide these terms, effectively multiplying by one, which simplifies things beautifully: $\frac{9}{6x^2 - q} \cdot \frac{5(6x^2 - q)}{54} = \frac{9}{1} \cdot \frac{5}{54}$

STEP 6

Now, we have $\frac{9 \cdot 5}{54}$ .
Let's simplify this.
We can rewrite $54$ as $9 \cdot 6$ , so we have: $\frac{9 \cdot 5}{9 \cdot 6}$ We can divide the numerator and denominator by 9, which is like multiplying by $\frac{1}{9}$ , giving us: $\frac{5}{6}$

STEP 7

Our final simplified answer is $\frac{5}{6}$ .

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QuestionDivide. $\frac{9}{6 x^{2}-q} \div \frac{54}{30 x^{2}-5 q}$ $\frac{9}{6 x^{2}-q} \div \frac{54}{30 x^{2}-5 q}=$ $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

STEP 2

1. Rewrite as Multiplication
2. Factor the Expressions
3. Simplify the Expression

STEP 3

Remember, dividing by a fraction is the same as multiplying by its reciprocal, or "flip and multiply." So, let's flip the second fraction and change the division to multiplication: $\frac{9}{6x^2 - q} \div \frac{54}{30x^2 - 5q} = \frac{9}{6x^2 - q} \cdot \frac{30x^2 - 5q}{54}$

STEP 4

Look at the numerator of the second fraction, $30x^2 - 5q$ .
We can factor out a 5, giving us $5(6x^2 - q)$ .
This is great because we have a similar expression in the denominator of the first fraction!
Our expression now looks like: $\frac{9}{6x^2 - q} \cdot \frac{5(6x^2 - q)}{54}$

STEP 5

Notice how $(6x^2 - q)$ appears in both the numerator and the denominator.
We can divide these terms, effectively multiplying by one, which simplifies things beautifully: $\frac{9}{6x^2 - q} \cdot \frac{5(6x^2 - q)}{54} = \frac{9}{1} \cdot \frac{5}{54}$

STEP 6

Now, we have $\frac{9 \cdot 5}{54}$ .
Let's simplify this.
We can rewrite $54$ as $9 \cdot 6$ , so we have: $\frac{9 \cdot 5}{9 \cdot 6}$ We can divide the numerator and denominator by 9, which is like multiplying by $\frac{1}{9}$ , giving us: $\frac{5}{6}$

STEP 7

Our final simplified answer is $\frac{5}{6}$ .

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QuestionDivide. 96x2−q÷5430x2−5q\frac{9}{6 x^{2}-q} \div \frac{54}{30 x^{2}-5 q}6x2−q9​÷30x2−5q54​ 96x2−q÷5430x2−5q=\frac{9}{6 x^{2}-q} \div \frac{54}{30 x^{2}-5 q}=6x2−q9​÷30x2−5q54​= □\square□ (Simplify your answer.)

Studdy Solution

STEP 1

STEP 2

1. Rewrite as Multiplication2. Factor the Expressions3. Simplify the Expression

STEP 3

STEP 4

STEP 5

STEP 6

STEP 7

Our final simplified answer is 56\frac{5}{6}65​.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionDivide. $\frac{9}{6 x^{2}-q} \div \frac{54}{30 x^{2}-5 q}$ $\frac{9}{6 x^{2}-q} \div \frac{54}{30 x^{2}-5 q}=$ $\square$ (Simplify your answer.)

1. Rewrite as Multiplication
2. Factor the Expressions
3. Simplify the Expression

Our final simplified answer is $\frac{5}{6}$ .