Given-ab-cd-Prove that- 3a-5b3a-5b-3c-5d3c-5d

Prove that: 3a 5b3a+5b=3c 5d3c+5d Multiply both sides by nbsp;35' we get ⇒3a5b=3c5d ⇒3a+5b3a 5b=3c+5d3c 5d [by componendo and dividendo] ⇒(3a+5b)(3c 5d)=(3c+5 ...

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Standard X

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Kashmir

Given,ab=cd,P...

Question

Given, $\frac{a}{b} = \frac{c}{d},$
Prove that: $\frac{3 a - 5 b}{3 a + 5 b} = \frac{3 c - 5 d}{3 c + 5 d}$

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Solution

Prove that: $\frac{3 a - 5 b}{3 a + 5 b} = \frac{3 c - 5 d}{3 c + 5 d}$
Multiply both sides by $\frac{3}{5^{'}}$ we get
$\Rightarrow \frac{3 a}{5 b} = \frac{3 c}{5 d}$
$\Rightarrow \frac{3 a + 5 b}{3 a - 5 b} = \frac{3 c + 5 d}{3 c - 5 d}$
[by componendo and dividendo]
$\Rightarrow (3 a + 5 b) (3 c - 5 d) = (3 c + 5 d) (3 a - 5 b)$
$\Rightarrow \frac{3 c - 5 d}{3 c + 5 d} = \frac{3 a - 5 b}{3 a + 5 b}$
$\Rightarrow \frac{3 a - 5 b}{3 a + 5 b} = \frac{3 c - 5 d}{3 c + 5 d}$
Hence,proved.

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Q. If (3a + 8b) : (3c + 8d) = (3a − 8b) : (3c − 8d), then show that a, b, c, d are in proportion.

Q. Given

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

, prove that

\frac{3 a - 5 b}{3 a + 5 b} = \frac{3 c - 5 d}{3 c + 5 d}

Q. If

\frac{8 a - 5 b}{8 c - 5 d} = \frac{8 a + 5 b}{8 c + 5 d}

, then show that

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

Simplify:
$(a - 2 b + 5 c) (a - b) - (a - b - c) (2 a + 3 c) + (6 a + b) (2 c - 3 a - 5 b)$

If $\frac{8 a - 5 b}{8 c - 5 d} = \frac{8 a + 5 b}{8 c + 5 d}$ , then $\frac{a}{b} = \frac{c}{d}$

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Kashmir

Standard X History

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Given,ab=cd, Prove that: 3a−5b3a+5b=3c−5d3c+5d

Prove that: 3a−5b3a+5b=3c−5d3c+5d Multiply both sides by 35′ we get ⇒3a5b=3c5d ⇒3a+5b3a−5b=3c+5d3c−5d [by componendo and dividendo] ⇒(3a+5b)(3c−5d)=(3c+5d)(3a−5b) ⇒3c−5d3c+5d=3a−5b3a+5b ⇒3a−5b3a+5b=3c−5d3c+5d ​​​​​​​Hence,proved.

Given, $\frac{a}{b} = \frac{c}{d},$
Prove that: $\frac{3 a - 5 b}{3 a + 5 b} = \frac{3 c - 5 d}{3 c + 5 d}$