x: x+2/x+5=x/x+6 solve it
Answers
Answer:
Move
x + 6
x − 7
to the left side of the equation by subtracting it from both sides.
x − 2
x − 5
−
x
+
6
x
−
7
=
0
Simplify
x
−
2
x
−
5
−
x
+
6
x
−
7
.
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−
2
(
5
x
−
22
)
(
x
−
5
)
(
x
−
7
)
=
0
To write
x
−
2
x
−
5
as a fraction with a common denominator, multiply by
x
−
7
x
−
7
.
x
−
2
x
−
5
⋅
x
−
7
x
−
7
−
x
+
6
x
−
7
=
0
To write
−
x
+
6
x
−
7
as a fraction with a common denominator, multiply by
x
−
5
x
−
5
.
x
−
2
x
−
5
⋅
x
−
7
x
−
7
−
x
+
6
x
−
7
⋅
x
−
5
x
−
5
=
0
Write each expression with a common denominator of
(
x
−
5
)
(
x
−
7
)
, by multiplying each by an appropriate factor of
1
.
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(
x
−
2
)
(
x
−
7
)
(
x
−
5
)
(
x
−
7
)
−
(
x
+
6
)
(
x
−
5
)
(
x
−
5
)
(
x
−
7
)
=
0
Combine the numerators over the common denominator.
(
x
−
2
)
(
x
−
7
)
−
(
x
+
6
)
(
x
−
5
)
(
x
−
5
)
(
x
−
7
)
=
0
Simplify the numerator.
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2
(
−
5
x
+
22
)
(
x
−
5
)
(
x
−
7
)
=
0
Simplify with factoring out.
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−
2
(
5
x
−
22
)
(
x
−
5
)
(
x
−
7
)
=
0
Find the LCD of the terms in the equation.
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(
x
−
5
)
(
x
−
7
)
Multiply each term by
(
x
−
5
)
(
x
−
7
)
and simplify.
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−
10
x
+
44
=
0
Solve the equation.
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x
=
22
5
Step-by-step explanation:
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