Answer:
Option B.
Step-by-step explanation:
The given expression is
[tex]\dfrac{2a-7}{a}\times \dfrac{3a^2}{2a^2-11a+14}[/tex]
We need to find the product.
The given expression can be rewritten as
[tex]\dfrac{2a-7}{a}\times \dfrac{3a^2}{2a^2-7a-4a+14}[/tex]
[tex]\dfrac{2a-7}{a}\times \dfrac{3a^2}{a(2a-7)-2(2a-7)}[/tex]
[tex]=\dfrac{2a-7}{a}\times \dfrac{3a^2}{(2a-7)(a-2)}[/tex]
[tex]=\dfrac{(2a-7)3a^2}{a(2a-7)(a-2)}[/tex]
Cancel out the common factors.
[tex]=\dfrac{3a}{a-2}[/tex]
So, [tex]\dfrac{2a-7}{a}\times \dfrac{3a^2}{2a^2-11a+14}=\dfrac{3a}{a-2}[/tex]
Therefore, the correct option is B.
The product of the fractions as given is; 3a/(a-2)
The fractions given are;
[tex]\frac{2a - 7}{a} \times \frac{3 {a}^{2}}{2 {a}^{2} - 11a + 14} [/tex]
[tex]\frac{2a - 7}{a} \times \frac{3 {a}^{2}}{2 {a}^{2} - 7a - 4a + 14} [/tex]
So that we have;
3a²/a(a- 2)
= 3a/(a -2)
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