Question

$\huge\sf\blue{Question}$

$\frac{(2 + x)(x - 7}{(x - 5)(x + 4)} = 1$
✅Please solve the given equation

✅also verify your answer

✅solve it step by step

$\small\sf\green{ asked \: by \: vinay}$
​

Answer 1

Answer:

$\huge{ \underline{ \frak{ \green{Question}}}}$

$\sf\frac{(2 + x)(x - 7)}{(x - 5)(x + 4)} = 1$

$\huge{ \underline{ \frak{ \green{Answer}}}}$

$\frak{ \underline{ \green{Identity \: used :}}}$

(x + a)(x + b) = x² + (a + b)x + ab

$\frak{ \underline{ \green{Soln :}}}$

$\sf \: \rightarrow\frac{(2 + x)(x - 7)}{(x - 5)(x + 4)} = 1$

$\rightarrow \sf \frac{(x + 2)(x - 7)}{(x - 5)(x + 4)} = 1$

$\rightarrow \sf \frac{{x}^{2} + (2 - 7)x - 14}{x {}^{2} + ( - 5 + 4)x - 20} = 1$

$\rightarrow \sf\frac{x {}^{2} - 5x - 14 }{ {x}^{2} - x - 20 } = 1$

$\rightarrow \sf \: {x}^{2} - 5x - 14 = {x}^{2} - x - 20$

$\rightarrow \sf \: - 5x - 14 = - x - 20$

$\rightarrow \sf5x + 14 = x + 20$

$\rightarrow\sf 5x - x = 20 - 14$

$\rightarrow \sf \: 4x = 6$

$\rightarrow \sf \: x = \frac{6}{4} = \frac{3}{2}$

$\boxed{ \frak{ \green{∴\: x = \frac{3}{2} }}}$

${\underline{ \frak{\green{ Verifying \: solution }}}}$

L.H.S

$\rightarrow \sf \frac{(2 + \frac{3}{2} )( \frac{3}{2} - 7) }{( \frac{3}{2} - 5)( \frac{3}{2} + 4)}$

$\rightarrow \sf \frac{( \frac{ 7}{2})( \frac{ - 11}{2}) }{( \frac{ - 7}{2} )( \frac{11}{2} )}$

$\rightarrow \sf \frac{ \frac{ - 77}{4} }{ \frac{ - 77}{4} }$

$\rightarrow \sf1$

L.H.S = R.H.S

Hence verified

$\green{ \frak{hope \: it \: helps...}}$

$\huge{ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}$