[tex]1.) \: 5ab[/tex]
[tex]2.) \: \frac{3ax}{7} [/tex]
[tex]3.) \: \frac{ - 3y + 27}{5x} [/tex]
[tex]4.) \: \frac{4z}{3ay} [/tex]
[tex]5.) \: \frac{3x {}^{3} - x + 2 }{x} [/tex]
Step-by-step explanation:
1.) Cancel out 3abc in both numerator and denominator.
[tex] - \frac{5ab}{ - 1} [/tex]
Anything divided by - 1 gives it's opposite.
[tex] - ( - 5ab)[/tex]
The opposite of –5ab is 5ab.
[tex]5ab[/tex]
2.) Cancel out 6ayz³ in both numerator and denominator.
[tex] \frac{3ayz}{7} [/tex]
3.) Cancel out 3 (y - 9)² x³ in both numerator and denominator.
[tex] \frac{ 3(y - 9)}{5x} [/tex]
Use the distributive property to multiply –3 by y –9.
[tex] \frac{3y + 27}{5x} [/tex]
4.) To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
[tex] \frac{d}{dx} (( - \frac{20zy {}^{4} }{15ay {}^{5} })x {}^{3 - 2} )[/tex]
Do the arithmetic.
[tex] \frac{d}{dx} (( - \frac{4z}{3ay} )x {}^{1} )[/tex]
The derivative of a polynomial is the sum of the derivatives of it's terms. The derivative of a constant term is 0. The derivative of ax^n is nax^n-1.
[tex]( - \frac{4z}{3ay} )x {}^{1 - 1} [/tex]
[tex]( - \frac{4z}{3ay} )x {}^{0} [/tex]
For any term t except 0, t^0 = 1.
[tex]( - \frac{4z}{3ay} ) \times 1[/tex]
For any term t, t × 1 = t and 1t = t.
5.) Factor the expressions that are not already factored in:
[tex] \frac{9x {}^{3} - 3x + 6 }{3x} [/tex]
[tex] - \frac{3(x + 1)(3x {}^{2} - 3x + 2}{3x} [/tex]
Cancel out 3 in both numerator and denominator.
[tex] - \frac{(x + 1)(3x {}^{2} - 3x + 2) }{x} [/tex]
Use the distributive property to multiply x + 1 by 3x² - 3x + 2 and combine like terms.
[tex] - \frac{3x {}^{3} - x + 2}{x} [/tex]
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