Question

{(x+6)/(x+5)}-{(2x-1)/(x-4)}+{(x+4)/(x-2)}=0
Solve for x plz

Answer 1

Answer:

x=(-2)

Step-by-step explanation:

${\mapsto\sf \dfrac{x+6}{x+5} - \dfrac{2x-1}{x-4}+ \dfrac{x+4}{x-2} = 0}$

• Taking LCM

${ \sf \mapsto\dfrac{\pink{\{(x-4)(x-2)\} (x-6) } - \orange{\{(x+5)(x-2)\} -(2x-1) } + \green{\{(x+5)(x-4)\} (x+4) } }{ \gray{(x-5)(x-4)(x-2)} } = 0}$

${ \sf \mapsto\dfrac{\pink{( {x}^{2} - 6x + 8)(x-6) } + \orange{( {x}^{2} + 3x - 10) ( - 2x + 1) } + \green{( {x}^{2} + x - 20) (x+4) } }{ \gray{(x-5)(x-4)(x-2)} } \times\blue{(x-5)(x-4)(x-2)} = 0 \times \blue{(x-5)(x-4)(x-2)}}$

${ \sf \mapsto {x}^{3} - 28x + 48 - 2 {x}^{3} - 5 {x}^{2} + 23 x - 10 + {x}^{3} + 5 {x}^{2} - 16x - 80 = 0}$

${ \sf \mapsto 2{x}^{3} - 2 {x}^{3} - 28x + 7x + 48 - 90 - \cancel{ 5 {x}^{2}} + \cancel{ 5 {x}^{2}} = 0}$

${ \sf \mapsto - 21x - 42 = 0}$

${ \sf \mapsto - 21x = 42 }$

${ \sf \mapsto 21x = - 42 }$

${ \sf \mapsto x = \dfrac{ - 42}{21} }$

${ \bf \mapsto x = - 2 }$

• $\\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\gray{\begin{gathered}\tiny\begin{gathered}\small{\small{\small{\small{\small{\small{\small{\small{\small{\small{\begin{gathered}\begin{gathered}\begin{gathered}\\\\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\red{ \bigstar} \: \underline{\bf{\orange{More \: Useful \: Formula}}}\\ {\boxed{\begin{array}{cc}\dashrightarrow \sf(a + b)^{2} = {a}^{2} + {b}^{2} + 2ab \\\\\dashrightarrow \sf(a - b)^{2} = {a}^{2} + {b}^{2} - 2ab \\\\\dashrightarrow \sf(a + b)(a - b) = {a}^{2} - {b}^{2} \\\\\dashrightarrow \sf(a + b) ^{3} = {a}^{3} + b^{3} + 3ab(a + b) \\\\ \dashrightarrow\sf(a - b) ^{3} = {a}^{3} - b^{3} - 3ab(a - b) \\ \\\dashrightarrow\sf a ^{3} + {b}^{3} = (a + b)(a ^{2} + {b}^{2} - ab) \\\\\dashrightarrow \sf a ^{3} - {b}^{3} = (a - b)(a ^{2} + {b}^{2} + ab )\\\\\dashrightarrow \sf{a²+b²=(a+b)²-2ab}\\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}}}}}}}}}}}\end{gathered}\end{gathered}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

Answer 2

Answer:

↪️ x = -2.

✥ For the explanation see the attachment photo.

✥ Don't forget to thanks

✥ Mark as brainlist.