expandir (5(x+h)^2+4(x+h))/h

Solução

expandir

\frac{5 ( x + h ) ^{2} + 4 ( x + h )}{h}

\frac{5 x ^{2}}{h} + 10 x + 5 h + \frac{4 x}{h} + 4

Passos da solução

\frac{5 ( x + h ) ^{2} + 4 ( x + h )}{h}

(x + h)^{2} = x^{2} + 2 x h + h^{2}

= \frac{5 ( x ^{2} + 2 x h + h ^{2} ) + 4 ( x + h )}{h}

Expandir

5 (x^{2} + 2 x h + h^{2}) + 4 (x + h) : 5 x^{2} + 10 x h + 5 h^{2} + 4 x + 4 h

= \frac{5 x ^{2} + 10 x h + 5 h ^{2} + 4 x + 4 h}{h}

Aplicar as propriedades das frações:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{5 x ^{2} + 10 x h + 5 h ^{2} + 4 x + 4 h}{h} = \frac{5 x ^{2}}{h} + \frac{10 x h}{h} + \frac{5 h ^{2}}{h} + \frac{4 x}{h} + \frac{4 h}{h}

= \frac{5 x ^{2}}{h} + \frac{10 x h}{h} + \frac{5 h ^{2}}{h} + \frac{4 x}{h} + \frac{4 h}{h}

Cancelar

\frac{10 x h}{h} : 10 x

= \frac{5 x ^{2}}{h} + 10 x + \frac{5 h ^{2}}{h} + \frac{4 x}{h} + \frac{4 h}{h}

Cancelar

\frac{5 h ^{2}}{h} : 5 h

= \frac{5 x ^{2}}{h} + 10 x + 5 h + \frac{4 x}{h} + \frac{4 h}{h}

Cancelar

\frac{4 h}{h} : 4

= \frac{5 x ^{2}}{h} + 10 x + 5 h + \frac{4 x}{h} + 4

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