Reducing Equations to Simpler Form

When linear equations are in fractions then we can reduce them to a simpler form by-

  • Taking the LCM of the denominator
  • Multiply the LCM on both the sides, so that the number will reduce without the denominator and we can solve them by the above methods.

Example
Solve the linear equation

\mathrm{\dfrac{x}{2}-\dfrac{1}{5}=\dfrac{x}{3}+\dfrac{1}{4}+1}

Solution
As the equation is in complex form, we have to reduce it into a simpler form.

Multiply both the sides by 60,

\mathrm{\dfrac{x}{2}-\dfrac{1}{5}=\dfrac{x}{3}+\dfrac{1}{4}+1}

\mathrm{30x -12 = 20x + 15 + 60}

Bring all the variables on the LHS and all the constants on the RHS

\mathrm{30x - 20x = 15 + 12 + 60}

\mathrm{10x = 87}

Dividing both the sides by 10

\mathrm{x = 8.7}

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