solve 1/x+2 + 1/x+3 = 2/x+9
Answers
Answer:
x= -33/13
Step-by-step explanation:
1/x+2 + 1/x+3 = 2/x+9;
[(x+3)+(x+2)]/(x+3)(x+2)=2/x+9;
(2x+5)(x+9)=2(x+2)(x+3);
2x^2+5x+18x+45=2x^2+10x+12
2x^2 cancel out;
23x+45=10x+2;
13x=12-45;
x= -33/13
Answer:
STEPS USING THE QUADRATIC FORMULA
x+2
1
+
x+3
1
=
x+9
1
Variable x cannot be equal to any of the values −9,−3,−2 since division by zero is not defined. Multiply both sides of the equation by (x+2)(x+3)(x+9), the least common multiple of x+2,x+3,x+9.
(x+3)(x+9)+(x+2)(x+9)=(x+2)(x+3)
Use the distributive property to multiply x+3 by x+9 and combine like terms.
x
2
+12x+27+(x+2)(x+9)=(x+2)(x+3)
Use the distributive property to multiply x+2 by x+9 and combine like terms.
x
2
+12x+27+x
2
+11x+18=(x+2)(x+3)
Combine x
2
and x
2
to get 2x
2
.
2x
2
+12x+27+11x+18=(x+2)(x+3)
Combine 12x and 11x to get 23x.
2x
2
+23x+27+18=(x+2)(x+3)
Add 27 and 18 to get 45.
2x
2
+23x+45=(x+2)(x+3)
Use the distributive property to multiply x+2 by x+3 and combine like terms.
2x
2
+23x+45=x
2
+5x+6
Subtract x
2
from both sides.
2x
2
+23x+45−x
2
=5x+6
Combine 2x
2
and −x
2
to get x
2
.
x
2
+23x+45=5x+6
Subtract 5x from both sides.
x
2
+23x+45−5x=6
Combine 23x and −5x to get 18x.
x
2
+18x+45=6
Subtract 6 from both sides.
x
2
+18x+45−6=0
Subtract 6 from 45 to get 39.
x
2
+18x+39=0
This equation is in standard form: ax
2
+bx+c=0. Substitute 1 for a, 18 for b, and 39 for c in the quadratic formula,
2a
−b±
b
2
−4ac
.
x=
2
−18±
18
2
−4×39
Square 18.
x=
2
−18±
324−4×39
Multiply −4 times 39.
x=
2
−18±
324−156
Add 324 to −156.
x=
2
−18±
168
Take the square root of 168.
x=
2
−18±2
42
Now solve the equation x=
2
−18±2
42
when ± is plus. Add −18 to 2
42
.
x=
2
2
42
−18
Divide −18+2
42
by 2.
x=
42
−9
Now solve the equation x=
2
−18±2
42
when ± is minus. Subtract 2
42
from −18.
x=
2
−2
42
−18
Divide −18−2
42
by 2.
x=−
42
−9
The equation is now solved.
x=
42
−9
x=−
42
−9