Question

Solve the equation:1\4x+1\6x=1\2x+3\4

Answer 1

Hey there!

Solution:


$\frac{1}{4x} + \frac{1}{6x} = \frac{1}{2x} + \frac{3}{4} \\ \\ Taking\: LCM\: on \:L.H.S \:side\\ \\ \frac{3 + 2}{12x} = \frac{1}{2x} + \frac{3}{4} \\ \\ \frac{5}{12x} = \frac{1}{2x} + \frac{3}{4} \\ \\ \frac{5}{12x} - \frac{1}{2x} = \frac{3}{4} \\ \\ Again \:Taking\: LCM \:on \:L.H.S : \\ \\ \frac{5 - 6}{12x} = \frac{3}{4} \\ \\ \frac{-1}{12x} = \frac{3}{4}\\ \\ Cross\: Multiplying:\\ \\ ( -1 ) ( 4 ) = 3 ( 12x ) \\ \\ -4 = 36x \\ \\x = \frac{-4}{36} \\ \\ x = \frac{-1}{9}$


#Be Brainly.

Answer 2

$\Huge\mathbb\colorbox{gold}{{\color{black}{Aɴsᴡᴇʀ ♡}}}$

$\bf\underline{\underline{{GIVEN :}}}$

$\bigstar \: \Large \rm \frac{1}{4x} + \frac{1}{6x} = \frac{1}{2x} + \frac{3}{4}$

$\bf\underline{\underline{{TO \: FIND :}}}$

$\bigstar \: Solve : \: \Large \rm \frac{1}{4x} + \frac{1}{6x} = \frac{1}{2x} + \frac{3}{4}$

$\bf\underline{\underline{{SOLUTION :}}}$

$\Large \rm \frac{1}{4x} + \frac{1}{6x} = \frac{1}{2x} + \frac{3}{4}$

Taking L.C.M on L.H.S,

$\Large \rm→\frac{3 + 2}{12x} = \frac{1}{2x} + \frac{3}{4} \\ \\ \Large \rm\Large \rm→ \frac{5}{12x} = \frac{1}{2x} + \frac{3}{4} \\ \\ \Large \rm→ \frac{5}{12x} - \frac{1}{2x} = \frac{3}{4}$

Again Taking L.C.M on L.H.S,

$\Large \rm→ \frac{5 - 6}{12x} = \frac{3}{4} \\ \\ \Large \rm→ \frac{ - 1}{12x} = \frac{3}{4}$

Now doing Cross Multiplication,

$\Large \rm→( - 1)(4) = 3(12x) \\ \\ \Large \rm→ - 4 = 36x \\ \\ \Large \rm→x = \frac{ - 4}{36} \\ \\ \Large \rm→x = \frac{ - 1}{9}$

Hope it Helps Buddy ♥️