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Answered

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simplify the sum plz

Simplify The Sum Plz class=

Sagot :

mhanifa

Answer:

  • (a² + b²)/a³b

Step-by-step explanation:

Simplify the given expression:

  • a³b⁵/b⁴a⁶ + a⁸b⁶/b⁷a⁹

The first fraction simplifies as:

  • b/a³ by cancelling a³ and b⁴

The second fraction simplifies as:

  • 1/ab by cancelling a⁸ and b⁶

The sum becomes:

  • b/a³ + 1/ab =                     Common denominator is a³b
  • b²/a³b + a²/a³b =              Multiply the first fraction by b, the second by a²
  • (a² + b²)/a³b
MisterBrian

Answer:

[tex]\Huge\boxed{ \bf \dfrac{ {b}^{2} + {a}^{2} }{ {a}^{3}b }} [/tex]

Step-by-step explanation:

Given expression:

[tex] \sf \longmapsto \dfrac{ {a}^{3} {b}^{5} }{b {}^{4} {a}^{6} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} } [/tex]

Solution:

[tex] \sf \longmapsto \dfrac{ {a}^{3} {b}^{5} }{b {}^{4} {a}^{6} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} } [/tex]

Cancel a^3 and a^6 on the left hand side of plus sign, which results to a^3.

[tex] \sf \longmapsto\dfrac{ \cancel{{a}^{3}} {b}^{5} }{b {}^{4} \cancel{{a}^{6}} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} } [/tex]

That is,

[tex] \sf \longmapsto \dfrac{b {}^{5} }{b {}^{4} a {}^{3} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} } [/tex]

Cancel b^5 and 5^4 on the LHS of plus sign, which results to b.

[tex]\sf \longmapsto \dfrac {\cancel{b {}^{5} }}{ \cancel{b {}^{4}} a {}^{3} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} } [/tex]

That is,

[tex]\sf \longmapsto \dfrac{b }{ a {}^{3} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} } [/tex]

Now cancel a^8 and a^9 on the RHS of Plus sign, which results to a.

[tex] \sf \longmapsto\dfrac{b }{ a {}^{3} } + \dfrac{ \cancel{{a}^{8}} {b}^{6} }{b {}^{7} \cancel{a {}^{9}} }[/tex]

That is,

[tex] \sf \longmapsto \: \dfrac{b }{ a {}^{3} } + \dfrac{ {b}^{6} }{b {}^{7} a {}^{} }[/tex]

Cancel b^6 and b^7 on the RHS of the Plus sign, which results to b.

[tex] \sf \longmapsto\dfrac{b }{ a {}^{3} } + \dfrac{ \cancel{ {b}^{6}} }{ \cancel{b {}^{7}} a {}^{} }[/tex]

That is,

[tex]\sf \longmapsto\dfrac{b }{ a {}^{3} } + \cfrac {1}{ {b {}^{1}} a {}^{} }[/tex]

Simply add:-

Rewrite into:

[tex] \sf \longmapsto \: \dfrac{ b {}^{} }{a {}^{3} } + \cfrac{1}{a \times b} [/tex]

Combine the numerators over LCD(a^3)

[tex] \sf \longmapsto \: \dfrac{ {b}^{2} + {a}^{2} }{ {a}^{3}b } [/tex]

Or it can also be rewritten as,

[tex] \sf \longmapsto \: \dfrac{ {a}^{2} + {b}^{2} }{ {a}^{3}b } [/tex]

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I hope this helps!

Please let me know if you have any questions

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