1upon x +4-1 upon x-7=11 upon 30 find the root
Answers
Answer:
Answer:
The solution of the expression is x=2,1.
Step-by-step explanation:
Given : Expression \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}
x+4
1
−
x−7
1
=
30
11
where x\neq -4,7x
=−4,7
To find : Solve the expression by factoring?
Solution :
Expression \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}
x+4
1
−
x−7
1
=
30
11
Taking LCM,
\frac{x-7-x-4}{(x+4)(x-7)}=\frac{11}{30}
(x+4)(x−7)
x−7−x−4
=
30
11
\frac{-11}{(x+4)(x-7)}=\frac{11}{30}
(x+4)(x−7)
−11
=
30
11
Cross multiply,
(x+4)(x-7)=-\frac{30\times 11}{11}(x+4)(x−7)=−
11
30×11
(x+4)(x-7)=-30(x+4)(x−7)=−30
Multiply the term,
x^2-7x+4x-28=-30x
2
−7x+4x−28=−30
x^2-3x-28+30=0x
2
−3x−28+30=0
x^2-3x+2=0x
2
−3x+2=0
Apply middle term split,
x^2-2x-x+2=0x
2
−2x−x+2=0
x(x-2)-1(x-2)=0x(x−2)−1(x−2)=0
(x-2)(x-1)=0(x−2)(x−1)=0
(x-2)=0,(x-1)=0(x−2)=0,(x−1)=0
x=2,x=1x=2,x=1
Therefore, The solution of the expression is x=2,1.
Step-by-step explanation:
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