Question

solve the following equation using cross multiplication method
1/x+1/3(5/3x-7/x) =-1​

Answer 1

Question

Solve the following equation using cross multiplication method

$\bf\boxed{ \frac{1}{x} + \frac{1}{3} \: ( \frac{5}{3x} - \frac{7}{x}) = ( - 1)}$

Answer

$\bf{ \frac{1}{x} + \frac{1}{3} \: ( \frac{5}{3x} - \frac{7}{x}) = ( - 1)}$

$\nrightarrow\bf{ \frac{1}{x} + \frac{1}{3} \: (\frac{5x - 21x}{3x {}^{2}}) = ( - 1)}$

$\nrightarrow\bf{ \frac{1}{x} + \frac{1}{3} \: (\frac{ - 16x}{3x {}^{2}}) = ( - 1)}$

$\nrightarrow\bf{ \frac{3 + x}{3x} \: (\frac{ - 16x}{3x {}^{2}}) = ( - 1)}$

$\nrightarrow\bf{ \frac{3 + x}{3x} \: \times \frac{ - 16x}{3x {}^{2}} = ( - 1)}$

$\nrightarrow\bf{ \frac{3 + x}{3x} \: \times \frac{ - 16 \cancel x}{3 \cancel x {}^{2}} = ( - 1)}$

$\nrightarrow\bf{ \frac{3 + x}{3x} \: \times \frac{ - 16 }{3x } = ( - 1)}$

$\nrightarrow\bf{ \frac{(3 + x)( - 16)}{3x \times 3x} \: = ( - 1)}$

$\nrightarrow\bf{ \frac{( - 48 - 16x)}{6x {}^{2} } \: = ( - 1)}$

$\nrightarrow\bf{ - 48 - 16x = - 6x {}^{2} }$

$\nrightarrow\bf{6x {}^{2}- 48 - 16x = 0}$