Simplify: start fraction, 3, x, to the power 4 , minus, 15, x, cubed, minus, 15, x, squared, divided by, 3, x, squared, end fraction
3x
2
3x
4
−15x
3
−15x
2
Solve the problem just like the example below
⬇️
Simplify:
start fraction, minus, 18, z, to the power 5 , plus, 3, z, to the power 4 , plus, 18, z, cubed, plus, 9, z, squared, divided by, minus, 3, z, squared, end fraction
−3z
2
−18z
5
+3z
4
+18z
3
+9z
2
minus, start fraction, 18, z, to the power 5 , divided by, minus, 3, z, squared, end fraction, plus, start fraction, 3, z, to the power 4 , divided by, minus, 3, z, squared, end fraction, plus, start fraction, 18, z, cubed, divided by, minus, 3, z, squared, end fraction, plus, start fraction, 9, z, squared, divided by, minus, 3, z, squared, end fraction
−
−3z
2
18z
5
+
−3z
2
3z
4
+
−3z
2
18z
3
+
−3z
2
9z
2
minus, left parenthesis, minus, 6, z, cubed, right parenthesis, plus, left parenthesis, minus, z, squared, right parenthesis, plus, left parenthesis, minus, 6, z, right parenthesis, plus, left parenthesis, minus, 3, right parenthesis
−(−6z
3
)+(−z
2
)+(−6z)+(−3)
6, z, cubed, minus, z, squared, minus, 6, z, minus, 3
6z
3
−z
2
−6z−3
1 answer
To simplify the expression \( \frac{3x^4 - 15x^3 - 15x^2}{3x^2} \), we will separate the terms in the numerator divided by the denominator.
-
Start with the original expression:
\[
\frac{3x^4 - 15x^3 - 15x^2}{3x^2}
\]
-
Separate each term in the numerator:
\[
= \frac{3x^4}{3x^2} - \frac{15x^3}{3x^2} - \frac{15x^2}{3x^2}
\]
-
Simplify each fraction:
- For the first term:
\[
\frac{3x^4}{3x^2} = x^{4-2} = x^2
\]
- For the second term:
\[
\frac{15x^3}{3x^2} = \frac{15}{3} x^{3-2} = 5x
\]
- For the third term:
\[
\frac{15x^2}{3x^2} = \frac{15}{3} = 5
\]
-
Combine the simplified terms:
\[
= x^2 - 5x - 5
\]
Thus, the simplified form of the expression \( \frac{3x^4 - 15x^3 - 15x^2}{3x^2} \) is:
\[
\boxed{x^2 - 5x - 5}
\]
