Answers
Answer:
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Answer:
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Step-by-step explanation:
Answer:
\dfrac{5a^3b-3ab^2}{3b^2-5a^2b}=-a
3b
2
−5a
2
b
5a
3
b−3ab
2
=−a
Step-by-step explanation:
\dfrac{5a^3b-3ab^2}{3b^2-5a^2b}
3b
2
−5a
2
b
5a
3
b−3ab
2
\mathrm{Factor}\:5a^3b-3ab^2Factor5a
3
b−3ab
2
5a^3b-3ab^25a
3
b−3ab
2
\gray{\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c}Applyexponentrule:a
b+c
=a
b
a
c
\gray{a^3=aa^2,\:b^2=bb}a
3
=aa
2
,b
2
=bb
=5aa^2b-3abb=5aa
2
b−3abb
\gray{\mathrm{Factor\:out\:common\:term\:}ba}Factoroutcommontermba
=ba\left(5a^2-3b\right)=ba(5a
2
−3b)
=\dfrac{ba\left(5a^2-3b\right)}{3b^2-5a^2b}=
3b
2
−5a
2
b
ba(5a
2
−3b)
\mathrm{Factor}\:3b^2-5a^2bFactor3b
2
−5a
2
b
3b^2-5a^2b3b
2
−5a
2
b
\gray{\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c}Applyexponentrule:a
b+c
=a
b
a
c
\gray{b^2=bb}b
2
=bb
=3bb-5a^2b=3bb−5a
2
b
\gray{\mathrm{Factor\:out\:common\:term\:}b}Factoroutcommontermb
=b\left(3b-5a^2\right)=b(3b−5a
2
)
=\dfrac{ba\left(5a^2-3b\right)}{b\left(3b-5a^2\right)}=
b(3b−5a
2
)
ba(5a
2
−3b)
\mathrm{Cancel\:}\dfrac{ba\left(5a^2-3b\right)}{b\left(3b-5a^2\right)}Cancel
b(3b−5a
2
)
ba(5a
2
−3b)
\dfrac{ba\left(5a^2-3b\right)}{b\left(3b-5a^2\right)}
b(3b−5a
2
)
ba(5a
2
−3b)
\gray{3b-5a^2\:=\:-\left(5a^2-3b\right)}3b−5a
2
=−(5a
2
−3b)
=\dfrac{ab\left(5a^2-3b\right)}{-b\left(5a^2-3b\right)}=
−b(5a
2
−3b)
ab(5a
2
−3b)
\gray{\mathrm{Refine}}Refine
=-\dfrac{ba\left(5a^2-3b\right)}{b\left(5a^2-3b\right)}=−
b(5a
2
−3b)
ba(5a
2
−3b)
\gray{\mathrm{Cancel\:the\:common\:factor:}\:b}Cancelthecommonfactor:b
=-\dfrac{a\left(5a^2-3b\right)}{5a^2-3b}=−
5a
2
−3b
a(5a
2
−3b)
\gray{\mathrm{Cancel\:the\:common\:factor:}\:5a^2-3b}Cancelthecommonfactor:5a
2
−3b
=-a=−a