Asked by Mo Cain Jumaah on Jun 13, 2024
Verified
Combine and simplify. 102x−3+72x+3\frac { 10 } { 2 x - 3 } + \frac { 7 } { 2 x + 3 }2x−310+2x+37
A) 34x+9(2x−3) (2x+3) \frac { 34 x + 9 } { ( 2 x - 3 ) ( 2 x + 3 ) }(2x−3) (2x+3) 34x+9
B) 2(x+7) (2x−3) (2x+3) \frac { 2 ( x + 7 ) } { ( 2 x - 3 ) ( 2 x + 3 ) }(2x−3) (2x+3) 2(x+7)
C) 20x−21(2x−3) (2x+3) \frac { 20 x - 21 } { ( 2 x - 3 ) ( 2 x + 3 ) }(2x−3) (2x+3) 20x−21
D) 174x\frac { 17 } { 4 x }4x17
E) 17(2x−3) (2x+3) \frac { 17 } { ( 2 x - 3 ) ( 2 x + 3 ) }(2x−3) (2x+3) 17
Combine
To bring two or more elements together to form a single entity or result.
Simplify
Simplifying a mathematical expression or equation involves executing operations and merging similar terms to present it in its most basic form.
- Undertake the tasks of adding and subtracting within the context of algebraic fractions.
Verified Answer
HZ
Hadia ZafarJun 18, 2024
Final Answer :
A
Explanation :
To add the two fractions, we need to find a common denominator.
The common denominator is:
(2x−3)(2x+3)(2x-3)(2x+3)(2x−3)(2x+3)
Now we can write:
102x−3+72x+3=10(2x+3)(2x−3)(2x+3)+7(2x−3)(2x−3)(2x+3)\frac{10}{2x-3}+\frac{7}{2x+3}=\frac{10(2x+3)}{(2x-3)(2x+3)}+\frac{7(2x-3)}{(2x-3)(2x+3)}2x−310+2x+37=(2x−3)(2x+3)10(2x+3)+(2x−3)(2x+3)7(2x−3)
Simplifying the numerators, we get:
20x+30(2x−3)(2x+3)+14x−21(2x−3)(2x+3)\frac{20x+30}{(2x-3)(2x+3)}+\frac{14x-21}{(2x-3)(2x+3)}(2x−3)(2x+3)20x+30+(2x−3)(2x+3)14x−21
Now we can add the fractions to get:
(20x+30)+(14x−21)(2x−3)(2x+3)=34x+9(2x−3)(2x+3)\frac{(20x+30)+(14x-21)}{(2x-3)(2x+3)}=\frac{34x+9}{(2x-3)(2x+3)}(2x−3)(2x+3)(20x+30)+(14x−21)=(2x−3)(2x+3)34x+9
Therefore, the answer is A.
The common denominator is:
(2x−3)(2x+3)(2x-3)(2x+3)(2x−3)(2x+3)
Now we can write:
102x−3+72x+3=10(2x+3)(2x−3)(2x+3)+7(2x−3)(2x−3)(2x+3)\frac{10}{2x-3}+\frac{7}{2x+3}=\frac{10(2x+3)}{(2x-3)(2x+3)}+\frac{7(2x-3)}{(2x-3)(2x+3)}2x−310+2x+37=(2x−3)(2x+3)10(2x+3)+(2x−3)(2x+3)7(2x−3)
Simplifying the numerators, we get:
20x+30(2x−3)(2x+3)+14x−21(2x−3)(2x+3)\frac{20x+30}{(2x-3)(2x+3)}+\frac{14x-21}{(2x-3)(2x+3)}(2x−3)(2x+3)20x+30+(2x−3)(2x+3)14x−21
Now we can add the fractions to get:
(20x+30)+(14x−21)(2x−3)(2x+3)=34x+9(2x−3)(2x+3)\frac{(20x+30)+(14x-21)}{(2x-3)(2x+3)}=\frac{34x+9}{(2x-3)(2x+3)}(2x−3)(2x+3)(20x+30)+(14x−21)=(2x−3)(2x+3)34x+9
Therefore, the answer is A.
Learning Objectives
- Undertake the tasks of adding and subtracting within the context of algebraic fractions.