Question

8/a este egal cu 6/b

a) 4a+2b/2a-b = ?
b)a²-b²/a²+b² = ?

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Answer 1

Explicație pas cu pas:

$\dfrac{8}{a} = \dfrac{6}{b} \iff \dfrac{a}{8} = \dfrac{b}{6} = k$

$a = 8k \\ b = 6k$

a)

$\dfrac{4a + 2b}{2a - b} = \dfrac{32k + 12k}{16k - 6k} = \dfrac{44k}{10k} = \dfrac{22}{5}$

b)

$\dfrac{ {a}^{2} - {b}^{2} }{ {a}^{2} + {b}^{2}} = \dfrac{64 {k}^{2} - 36{k}^{2} }{ 64 {k}^{2} + 36{k}^{2}} = \dfrac{28{k}^{2} }{100{k}^{2}} = \dfrac{7}{25}$