Question

solve the this equation

Answer 1

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Answer 2

Required solution :

Given equation,

• $\red{\boxed{ \sf{ \frac{m + 3}{m - 2} \: = \: \frac{m + 5}{m - 5} }}}$

Cross multiplying them,

$\longmapsto \: \sf{(m + 3)(m - 5) \: = \: (m + 5)(m - 2)}$

$\longmapsto \: \sf{(m + 3) \times (m - 5) \: = \: (m + 5) \times (m - 2)}$

Solving for L.H.S. :-

$\longmapsto \: \sf{m(m - 5) + 3(m - 5)}$

$\longmapsto \: \sf{m \times (m - 5) + 3 \times (m - 5)}$

$\longmapsto \: \sf{m {}^{2} - \: 5m + \: 3m \: - \: 15}$

$\longmapsto \: \boxed{\sf{m {}^{2} - \: 2m \: - \: 15}}$

Solving for R.H.S. :

$\longmapsto \: \sf{m(m - 2) + 5(m - 2)}$

$\longmapsto \: \sf{m \times (m - 2) + 5 \times (m - 2)}$

$\longmapsto \: \sf{m {}^{2} - 2m + 5m - 10}$

$\longmapsto \: \boxed{\sf{m {}^{2} + 3m - 10}}$

Now, keeping them equal.

$: \: \implies \: \sf{m {}^{2} - 2m - 15 = m {}^{2} + 3m - 10}$

Transposing m² to L.H.S.,

$: \: \implies \: \sf{m {}^{2} - m {}^{2} - 2m - 15 =3m - 10}$

$: \: \implies \: \sf{- 2m - 15 =3m - 10}$

Transposing 3m to L.H.S., it would be negative.

$: \: \implies \: \sf{- 2m - 3m - 15 =- 10}$

$: \: \implies \: \sf{ - 5m - 15 =- 10}$

Now, at last transposing -15 to R.H.S. and it would be positive.

$: \: \implies \: \sf{ - 5m =15- 10}$

$: \: \implies \: \sf{ - 5m = 5}$

$: \: \implies \: \sf{m = - \dfrac{5}{5} }$

$: \: \implies \: \sf{m = - \cancel\dfrac{5}{5} }$

$: \: \implies \: \red{\bf{m = - 1}}$

Therefore,

• Value of m is -1