If dfrac-5-x-3- - dfrac-1-x-dfrac-1-2x- calculate the value of x-dfrac-3-14-dfrac-6-13-dfrac-9-7-dfrac-3-4-dfrac-1-3-

Given- 5x-3-1x-12xTaking RHS-1x-12xLCM of these is 2x-x21D2-22x-12x-x21D2-32xNow taking LHS-5x-3It is given- LHS - RHS5x-3-32x-x21D2-5-xD7-2x-3-xD7-x-3-x21D2-10x-3x-9-x21D2-x-97

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Standard VIII

Mathematics

Reducing Equations to Simpler Form

Question

If $\frac{5}{x + 3} = \frac{1}{x} + \frac{1}{2 x}$ , calculate the value of $x$ .
$\frac{3}{14}$
$\frac{6}{13}$
$\frac{9}{7}$
$\frac{3}{4}$
$\frac{1}{3}$

\frac{9}{7}

\frac{3}{14}

\frac{6}{13}

\frac{3}{4}

\frac{1}{3}

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Solution

Verified by Toppr

Given, $\frac{5}{x + 3} = \frac{1}{x} + \frac{1}{2 x}$
Taking RHS:
$\frac{1}{x} + \frac{1}{2 x}$
LCM of these is $2 x$
$\Rightarrow \frac{2}{2 x} + \frac{1}{2 x} \Rightarrow \frac{3}{2 x}$
Now taking LHS:
$\frac{5}{x + 3}$
It is given, LHS $=$ RHS
$\frac{5}{x + 3} = \frac{3}{2 x}$
$\Rightarrow 5 \times 2 x = 3 \times (x + 3) \Rightarrow 10 x = 3 x + 9 \Rightarrow x = \frac{9}{7}$

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(2) $(m - 4) (m + 6)$
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$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

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$x$	$f (x)$
$1$	$1$
$2$	$3$
$3$	$5$
$4$	$7$
$5$	$9$
$6$	$11$

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If 5x+3=1x+12x, calculate the value of x.314613973413

Given, 5x+3=1x+12xTaking RHS:1x+12xLCM of these is 2x⇒22x+12x⇒32xNow taking LHS:5x+3It is given, LHS = RHS5x+3=32x⇒5×2x=3×(x+3)⇒10x=3x+9⇒x=97

If $\frac{5}{x + 3} = \frac{1}{x} + \frac{1}{2 x}$ , calculate the value of $x$ .
$\frac{3}{14}$
$\frac{6}{13}$
$\frac{9}{7}$
$\frac{3}{4}$
$\frac{1}{3}$