Answer :
To simplify the expression [tex]\(\frac{49x^7 - 35x^5 - 42x^3}{7x^3}\)[/tex], we need to divide each term in the numerator by the term in the denominator. Let's go through the process step by step:
1. Divide the first term:
- [tex]\(49x^7\)[/tex] divided by [tex]\(7x^3\)[/tex]:
[tex]\[
\frac{49}{7} \times x^{7-3} = 7x^4
\][/tex]
- So the first term simplifies to [tex]\(7x^4\)[/tex].
2. Divide the second term:
- [tex]\(35x^5\)[/tex] divided by [tex]\(7x^3\)[/tex]:
[tex]\[
\frac{35}{7} \times x^{5-3} = 5x^2
\][/tex]
- So the second term simplifies to [tex]\(5x^2\)[/tex].
3. Divide the third term:
- [tex]\(42x^3\)[/tex] divided by [tex]\(7x^3\)[/tex]:
[tex]\[
\frac{42}{7} \times x^{3-3} = 6x^0 = 6
\][/tex]
- So the third term simplifies to [tex]\(6\)[/tex].
4. Combine the simplified terms:
- Combine these results to get the final simplified expression:
[tex]\[
7x^4 - 5x^2 - 6
\][/tex]
Thus, the simplified form of the given expression is [tex]\(7x^4 - 5x^2 - 6\)[/tex].
1. Divide the first term:
- [tex]\(49x^7\)[/tex] divided by [tex]\(7x^3\)[/tex]:
[tex]\[
\frac{49}{7} \times x^{7-3} = 7x^4
\][/tex]
- So the first term simplifies to [tex]\(7x^4\)[/tex].
2. Divide the second term:
- [tex]\(35x^5\)[/tex] divided by [tex]\(7x^3\)[/tex]:
[tex]\[
\frac{35}{7} \times x^{5-3} = 5x^2
\][/tex]
- So the second term simplifies to [tex]\(5x^2\)[/tex].
3. Divide the third term:
- [tex]\(42x^3\)[/tex] divided by [tex]\(7x^3\)[/tex]:
[tex]\[
\frac{42}{7} \times x^{3-3} = 6x^0 = 6
\][/tex]
- So the third term simplifies to [tex]\(6\)[/tex].
4. Combine the simplified terms:
- Combine these results to get the final simplified expression:
[tex]\[
7x^4 - 5x^2 - 6
\][/tex]
Thus, the simplified form of the given expression is [tex]\(7x^4 - 5x^2 - 6\)[/tex].
