1/x+1 + 3/5x+1= 5/x+4
Answers
Answer:
x=1,x=
17
−11
Step-by-step explanation:
Given : \frac{1}{x+1}+\frac{3}{5x+1}=\frac{5}{x+4}
x+1
1
+
5x+1
3
=
x+4
5
.......[1]
Solve : Equation [1]
\frac{1}{x+1}+\frac{3}{5x+1}=\frac{5}{x+4}
x+1
1
+
5x+1
3
=
x+4
5
Taking LCM
\frac{(5x+1)+3(x+1)}{(x+1)(5x+1)}=\frac{5}{x+4}
(x+1)(5x+1)
(5x+1)+3(x+1)
=
x+4
5
\frac{5x+1+3x+3)}{(5x^2+6x+1)}=\frac{5}{x+4}
(5x
2
+6x+1)
5x+1+3x+3)
=
x+4
5
\frac{8x+4}{(5x^2+6x+1)}=\frac{5}{x+4}
(5x
2
+6x+1)
8x+4
=
x+4
5
Cross multiply
(8x+4)\times(x+4)=(5x^2+6x+1)\times 5(8x+4)×(x+4)=(5x
2
+6x+1)×5
(8x^2+32x+4x+16)=(25x^2+30x+5)(8x
2
+32x+4x+16)=(25x
2
+30x+5)
8x^2+36x+16=25x^2+30x+58x
2
+36x+16=25x
2
+30x+5
8x^2-25x^2+36x-30x+16-5=08x
2
−25x
2
+36x−30x+16−5=0
-17x^2+6x+11=0−17x
2
+6x+11=0
17x^2-6x-11=017x
2
−6x−11=0
17x^2-17x+11x-11=017x
2
−17x+11x−11=0 (Middle term split)
(x-1)(17x+11)=0(x−1)(17x+11)=0
x=1 , x=\frac{-11}{17}x=
17
−11