Question

solve :- (i).7y+4/y+2 = -4/3​

Answer 1

Step-by-step explanation:

QUESTION:

\frac{7y + 4}{y + 2} = - 4y + 8

y+2

7y+4

=−4y+8

ANSWER:

We do the cross multiplication first;

7y + 4 = ( - 4y + 8)(y + 2)7y+4=(−4y+8)(y+2)

solving RHS side;

\begin{gathered}7y + 4 = y( - 4y + 8) + 2( - 4y + 8) \\ 7y + 4 = - 4 {y}^{2} + 8y - 8y + 16 \\ 7y + 4 = - 4 {y}^{2} + 16 \\ 4 {y}^{2} + 7y + 4 - 16 = 0 \\ 4 {y}^{2} + 7y - 12 = 0\end{gathered}

7y+4=y(−4y+8)+2(−4y+8)

7y+4=−4y

2

+8y−8y+16

7y+4=−4y

2

+16

4y

2

+7y+4−16=0

4y

2

+7y−12=0

factorised it;

we have to split the middle term in such a way that it's sum equal to b i.e 7 and product will be a ×c that is 48

\begin{gathered}4 {y}^{2} + 12y - 4y - 12 = 0 \\ 4y(y + 3) - 4(y + 3) \\ (4y - 4)(y + 3)\end{gathered}

4y

2

+12y−4y−12=0

4y(y+3)−4(y+3)

(4y−4)(y+3)

So;

\begin{gathered}4y - 4 = 0 \\ 4y = 4 \\ y = 1\end{gathered}

4y−4=0

4y=4

y=1

or

\begin{gathered}y + 3 = 0 \\ y = - 3\end{gathered}

y+3=0

y=−3

FINAL ANSWER;

\huge\red{y = 1 \: or \: - 3}y=1or−3

Answer 2

⭐Answer:

7y+4/y+2= -4/3

→ 3(7y+4) = -4(y+2)

→ 21y+12= -4y-8

→ 21y+4y=-8-12

→ 25y= -20

→ y= -20/25

→ y= -4/5