Question

simplify the sum plz

Answer 1

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

Answer 2

Answer:

$\Huge\boxed{ \bf \dfrac{ {b}^{2} + {a}^{2} }{ {a}^{3}b }}$

Step-by-step explanation:

Given expression:

$\sf \longmapsto \dfrac{ {a}^{3} {b}^{5} }{b {}^{4} {a}^{6} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} }$

Solution:

$\sf \longmapsto \dfrac{ {a}^{3} {b}^{5} }{b {}^{4} {a}^{6} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} }$

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

$\sf \longmapsto\dfrac{ \cancel{{a}^{3}} {b}^{5} }{b {}^{4} \cancel{{a}^{6}} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} }$

That is,

$\sf \longmapsto \dfrac{b {}^{5} }{b {}^{4} a {}^{3} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} }$

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

$\sf \longmapsto \dfrac {\cancel{b {}^{5} }}{ \cancel{b {}^{4}} a {}^{3} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} }$

That is,

$\sf \longmapsto \dfrac{b }{ a {}^{3} } + \dfrac{ {a}^{8} {b}^{6} }{b {}^{7} a {}^{9} }$

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

$\sf \longmapsto\dfrac{b }{ a {}^{3} } + \dfrac{ \cancel{{a}^{8}} {b}^{6} }{b {}^{7} \cancel{a {}^{9}} }$

That is,

$\sf \longmapsto \: \dfrac{b }{ a {}^{3} } + \dfrac{ {b}^{6} }{b {}^{7} a {}^{} }$

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

$\sf \longmapsto\dfrac{b }{ a {}^{3} } + \dfrac{ \cancel{ {b}^{6}} }{ \cancel{b {}^{7}} a {}^{} }$

That is,

$\sf \longmapsto\dfrac{b }{ a {}^{3} } + \cfrac {1}{ {b {}^{1}} a {}^{} }$

Simply add:-

Rewrite into:

$\sf \longmapsto \: \dfrac{ b {}^{} }{a {}^{3} } + \cfrac{1}{a \times b}$

Combine the numerators over LCD(a^3)

$\sf \longmapsto \: \dfrac{ {b}^{2} + {a}^{2} }{ {a}^{3}b }$

Or it can also be rewritten as,

$\sf \longmapsto \: \dfrac{ {a}^{2} + {b}^{2} }{ {a}^{3}b }$

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I hope this helps!

Please let me know if you have any questions