solve and verify:
x^2-(x+2)(x+3)/7x+1 = 2/3
Answers
Answer:
Please do follow me for answering
Step-by-step explanation:
Answer:-
\begin{gathered}\frac{ {x }^{2} - (x + 2)(x + 3) }{7x + 1} = \frac{2}{3} \\ \\ = > \frac{ {x}^{2} - ( {x}^{2} + 5x + 6) }{7x + 1} = \frac{2}{3} \\ \\ = > \frac{ {x }^{2} - {x}^{2} - 5x - 6 }{7x + 1} = \frac{2}{3} \\ \\ = > \frac{ - 5x - 6}{7x + 1} = \frac{2}{3} \\ \\ = > 3 \times (- 5x - 6) = 2 \times (7x + 1) \\ \\ = > - 15x - 18 = 14x + 2 \\ \\ = > 29x = - 20 \\ \\ = > x = \frac{ - 20}{29}\end{gathered}
7x+1
x
2
−(x+2)(x+3)
=
3
2
=>
7x+1
x
2
−(x
2
+5x+6)
=
3
2
=>
7x+1
x
2
−x
2
−5x−6
=
3
2
=>
7x+1
−5x−6
=
3
2
=>3×(−5x−6)=2×(7x+1)
=>−15x−18=14x+2
=>29x=−20
=>x=
29
−20
Now verification
Putting the value of X
\begin{gathered}= > \frac{ { \frac{ - 20}{29} }^{2} - { \frac{ - 20}{29} }^{2} - 5 \times \frac{ - 20}{29} - 6 }{7 \times \frac{ - 20}{29} + 1} = \frac{2}{3} \\ \\ = > \frac{ \frac{ 100}{29} - 6 }{ \frac{ - 140}{29} + 1} = \frac{2}{3} \\ \\ = > \frac{ \frac{100 - 174}{29} }{ \frac{ - 140 + 29}{29} } = \frac{2}{3} \\ \\ = > \frac{ \frac{ - 74}{29} }{ \frac{ - 111}{29} } = \frac{2}{3} \\ \\ = > \frac{ - 74}{ - 111} = \frac{2}{3} \\ \\ = > \frac{74}{111} = \frac{2}{3} \\ \\ = > \frac{37 \times 2}{37 \times 3} = \frac{2}{3} \\ \\ = > \frac{2}{3} = \frac{2}{3} \\ \\\end{gathered}
=>
7×
29
−20
+1
29
−20
2
−
29
−20
2
−5×
29
−20
−6
=
3
2
=>
29
−140
+1
29
100
−6
=
3
2
=>
29
−140+29
29
100−174
=
3
2
=>
29
−111
29
−74
=
3
2
=>
−111
−74
=
3
2
=>
111
74
=
3
2
=>
37×3
37×2
=
3
2
=>
3
2
=
3
2
Hence LHS = RHS verified
Step-by-step explanation:
x^2-x^2-3x-2x-6/7x+1=2/3
-5x-6=2/3×7x+1
3(-5x-6)=14x+2
-15x-18=14x+2
Multiply both side by (-);
15x+18=-14x-2
15x+14x=-2-18
29x=-20
x=-20/29