Question

Simplify......................​

Answer 1

$\implies {\blue {\boxed {\boxed {\purple {\sf { \frac{( {a}^{2} + {b}^{2} )}{a} }}}}}}$

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}$

$\frac{ {a}^{4} - {b}^{4} }{ {a}^{3} - a {b}^{2} }$

$\\= \frac{ ({ {a}^{2} })^{2} - { ({b}^{2} })^{2} }{a( {a}^{2} - {b}^{2} )}$

[ ∵ (a²)² = ${a}^{4}$ ]

$\\= \frac{( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2}) }{a( {a}^{2} - {b}^{2}) }$

$\\= \frac{( {a}^{2} + {b}^{2} )}{a}$

Note:

${a}^{2} - {b}^{2} = (a + b)(a - b)$

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