IDNLearn.com is committed to providing high-quality answers to your questions. Ask your questions and get detailed, reliable answers from our community of experienced experts.
Sagot :
To simplify the given expression [tex]\( \frac{2ax + 4bx}{3ay + 6by} \)[/tex], let's go through the steps in a detailed manner:
1. Identify Common Factors:
- In the numerator [tex]\( 2ax + 4bx \)[/tex], we notice that both terms [tex]\( 2ax \)[/tex] and [tex]\( 4bx \)[/tex] share a common factor of [tex]\(2x\)[/tex].
- In the denominator [tex]\( 3ay + 6by \)[/tex], we notice that both terms [tex]\( 3ay \)[/tex] and [tex]\( 6by \)[/tex] share a common factor of [tex]\(3y\)[/tex].
2. Factor Out the Common Terms:
- From the numerator [tex]\( 2ax + 4bx \)[/tex], factor out [tex]\(2x\)[/tex]:
[tex]\[ 2ax + 4bx = 2x(a + 2b) \][/tex]
- From the denominator [tex]\( 3ay + 6by \)[/tex], factor out [tex]\(3y\)[/tex]:
[tex]\[ 3ay + 6by = 3y(a + 2b) \][/tex]
3. Simplify the Expression:
- Substitute the factored forms back into the original fraction:
[tex]\[ \frac{2ax + 4bx}{3ay + 6by} = \frac{2x(a + 2b)}{3y(a + 2b)} \][/tex]
- Notice that the term [tex]\((a + 2b)\)[/tex] appears in both the numerator and the denominator. Since [tex]\((a + 2b)\)[/tex] is a common factor, it can be cancelled out, provided [tex]\(a + 2b \neq 0\)[/tex]:
[tex]\[ \frac{2x(a + 2b)}{3y(a + 2b)} = \frac{2x}{3y} \][/tex]
Thus, the simplified form of the given expression is:
[tex]\[ \frac{2ax + 4bx}{3ay + 6by} = \frac{2x}{3y} \][/tex]
1. Identify Common Factors:
- In the numerator [tex]\( 2ax + 4bx \)[/tex], we notice that both terms [tex]\( 2ax \)[/tex] and [tex]\( 4bx \)[/tex] share a common factor of [tex]\(2x\)[/tex].
- In the denominator [tex]\( 3ay + 6by \)[/tex], we notice that both terms [tex]\( 3ay \)[/tex] and [tex]\( 6by \)[/tex] share a common factor of [tex]\(3y\)[/tex].
2. Factor Out the Common Terms:
- From the numerator [tex]\( 2ax + 4bx \)[/tex], factor out [tex]\(2x\)[/tex]:
[tex]\[ 2ax + 4bx = 2x(a + 2b) \][/tex]
- From the denominator [tex]\( 3ay + 6by \)[/tex], factor out [tex]\(3y\)[/tex]:
[tex]\[ 3ay + 6by = 3y(a + 2b) \][/tex]
3. Simplify the Expression:
- Substitute the factored forms back into the original fraction:
[tex]\[ \frac{2ax + 4bx}{3ay + 6by} = \frac{2x(a + 2b)}{3y(a + 2b)} \][/tex]
- Notice that the term [tex]\((a + 2b)\)[/tex] appears in both the numerator and the denominator. Since [tex]\((a + 2b)\)[/tex] is a common factor, it can be cancelled out, provided [tex]\(a + 2b \neq 0\)[/tex]:
[tex]\[ \frac{2x(a + 2b)}{3y(a + 2b)} = \frac{2x}{3y} \][/tex]
Thus, the simplified form of the given expression is:
[tex]\[ \frac{2ax + 4bx}{3ay + 6by} = \frac{2x}{3y} \][/tex]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.